When will we get a dragon rider subclass?

Make it a series of feats with prerequisites that anyone can pick up. 

This would make a much more interesting world.

Different classes can ultimately gain different Dragons as friends/mounts. Never dominating the sapient Dragon. Other dragons would not like that, in fact they could view it as slavery.

You would have to have an insentient species just like other mounts. And nurf the mounts power. Breath weapons and flight for low level characters are very powerful.

A hundred ideas could be added to your world. But like others have said. Make sure the DM is not handing a player the cheat code.

The point about being non-sentient- or at least not previously extant beings who would have lives and goals outside of obeying your instructions- is covered by Drakewarden. The issue is that despite recent pushes for "setting neutral" content and a downgrade to the emphasis of lore, you can't meaningfully have a "real" dragon by the reckoning of most D&D players that also fits the mold of a subclass feature companion.

Can dragon-riders be good to explore underdark?

Maybe a dragonsteed-rider and this with climb speed could be useful to explore underground.

It might be super easy to figure out, but you certainly haven't. If you think a flying mount a level 5 or 7 is breaking the game, then you have no idea what base classes and existing subclasses can already do.

I have likened the dragon to paladin's "find steed" which can do the same thing, to sorcerer's "summon draconic spirit" which is substantially stronger, and there are easily craft able flying boots, carpets, brooms and many other ways to fly, even without concentration.

If you can't balance for stronger Drakewarden, you can't balance against half the classes.

To be honest, I would be ok with drake instead of a true dragon if it was stronger than before. But I also think dragon doesn't have to be such a problem. As I've said, the dragon can act more like warlock patron. They are usually crazy powerful and it doesn't make all adventures pointless. Have the dragon only start to grow into their power early on and act like a familiar, maybe even a non permanent one. Then it can be a remote presence that talks to you in the same way patron does (magically or through occasional visits) and you call call them once a day, or several times a day where they fly/teleport in and you can ride them properly. This impermanence would solve the role problem, they have their own stuff going on so they show up only when you really need them. It would also mechanically differentiate the ranger or fighter from other pet subclasses. And everyone thinks patrons are a great tool for DMs so having another class that's not a warlock with essentialy the same thing would allow for more plot hooks.

I've already said this elsewhere, but I'll reiterate. I'm not saying the dragon is supposed to be enslaved or anything similar. More like a warlock patron which instead of eldritch blast and 9th level spells gives you their help as a mount and partner in a limited fashion. 

You can give that to anyone. But it seems a shame to miss this opportunity to give classes that much need extra flavor and cool stuff, something cool and unique. Wizards don't need a dragon on top of what they already have. But fighters are desperately plain in my opinion, rangers are close behind. I guess figgters got better in 5.5, but still. Why not give them a bit more?

I've addressed this in like three separate comments. I will try to add an edit to the original post to clarify. It is not supposed to work exactly like a pet. More like warlock patron.

That's one of the arguments that are actually in favor of true dragon instead of a drake. Dragons can shape shift and they'd propably be only called in sometimes. Not a permanent companion. So eve if you're in a cramped space, they could appear as a humanoid caster summon, or they move through a corridor as a humanoid and turn into their real form once they get into an open cavern or room. That way you could use them in any situation.

You repeat “it would be like a patron” as if that solves all the problems.  It does not. Frankly, it probably creates more of them.

For starters, patrons are typically NPCs under the control of the DM, while the warlock’s powers are something the player controls.  That clearly defines the roles of each party and keeps there from bleeding lines between player and DM roles.  This is what makes them useful DM tools - they are an NPC that can always int react with the party when needed.

Where your idea breaks down is now you have the "patron” dragon a physical part of the party.  Now the line is blurred.  If it is to serve as a patron, then the Dm is to control it… but if it is a core set of mechanics, then the player does.  Introducing an NPC that is simultaneously both patron and pet who different people controlI at different points creates a party dynamic problem.

You also just have a problem with nonsensical situations becoming likely.  Let’s say the party is in a hard fight. Death looks possible. You have a situation where the dragon would effectively be saying “I am more powerful than this, but you have not unlocked the ability to use more of me. Guess we are all dying because, even though I am in the room right now, you don’t get these mechanics yet.”  Kind of takes some of the verisimilitude away if your “patron” is in the room and dies because they won’t use their whole strength.

Patrons work when they are distant figures conferring power.  They do not work so well as a joint PC/DM NPC who is also a frontline combatant in the party.

True dragons are far too powerful to be in a party. Thats it there is no argument you could make that would let them be in a party.
Flight and Breath weapons are far to powerful to hand to a PC. Even if its a nurfed very young dragon, mama will NOT let that happen.

A non intelligent Drake maybe. Not much of a breath weapon and very limited flight and carry capacity.

As a PC with a flying steed all I needed was the spell/item Feather Fall and I became an airborne assault force.
Tell the steed to go hide and I would just fall off dropping well behind enemy lines. Cast the FF spell/item on the way down and always land safe.
A few weeks of practice and I could guide my way to a specific roof in a town or castle.
Add in a few one gallon jugs of alchemist fire and you could get the idea of just how powerful a low level PC could get with just the flight ability.

Getting a dragon steed is normally something a PC would retire with as soon as acquiring. Your life long goal.

I keep repeating it because you keep not getting it. The dragon doesn't need to be in the party most of the time LIKE A PATRON. It's a presence in your mind, the dragon is doing their business, exercising their free will, then you summon it, for minutes or hours depending on your level and also how you want to balance it. You summon a hatchling first, later a very young and finally young dragon.

Controlling the dragon while it's summoned can be a problem, but so can anything. In practice it will hardly blur anything. It is DM controlled, but when summoned you can give it directions, like when you charm a monster, summon a creature, or the other myriad of situations that let you control other creatures. All kinds of live play campaigns have done the "allied creature" thing, including specifically dragons (including Critical role). So we have a proof of concept. It's okay to have an independent character that just acts in accord with you in combat.

Again THE DRAGON DOES NOT NEED TO BE WITH YOU ALWAYS. You and everyone else have been going on about how the dragon cannot be a slave. I agree, it should have its own stuff going on. And to help you it has to teleport or fly in. It can't do that always, or not immediately. So the party is in a hard fight, death is possible, but your dragon can't teleport at the moment (because your summoning feature is on cooldown) and you die. It can happen. OR, you have summoned the dragon, but guess what? You're fighting a lich, or Strahd, or Vecna, or an adult dragon and they all have much bigger CR than a young metallic dragon (which you would get at level 14), and definitely so much higher than a metallic hatchling which you would have like a third or half of the game. So yeah, the dragon can go all out, and you all still die. It's only issue if you deliberately give the subclass the ability to call on an adult or older dragon or if you make the dragon physically present all of the time. Neither of which is something I said or want. And don't try saying that even at level 14, young dragon is too powerful. I will again repeat myself, full casters are easily dragon level at that stage of the game. Not only can they raise long dead people, summon armies (via planar binding for example), to teleport, become immortal and make a copy of themselves. They can lock someone in a force cage or prismatic wall or wall of force, and grill a boss alive with radiation. Valor bard and bladesinger can upcast conjure minor elementals to cause something like 200 damage a turn, every turn, while still having huge AC. But yeah, summoning a large mount, or hell, even a huge mount that does like 30 damage per round, or uses a breath weapon that's a fireball and a half, yeah that would be terrible and overpowered.

I really wanted to have a good faith argument about it, but either you intentionally twist what I'm saying, or you plainly don't understand what I'm saying.

I will refer you to my other comments about full casters being much stronger than young and adult dragons, only being comparable (maybe) to ancient dragons. 

There is an argument to let them be in the party, and it's that. They're not that strong, PCs, especially casters, are. You're just wrong. I don't know what else to tell you.

Then what happens if it dies? Things like drakewardens or even find familiar don’t summon an actual creature, they summon a spirit that takes a physical form. Your version involves summoning an actual dragon who lives in the world. What happens if it dies?

Not to mention, dragons are very intelligent beings with their own agendas who will probably get increasingly annoyed at being pulled away from doing whatever they were doing.

And if you think an individual PC is as strong as a dragon, you’ve not dealt with a dragon that was run properly.

As a general rule, you should not get upset with others when your communication is to blame for your failing to convey your ideas.  Case in point, your posts are internally inconsistent and you keep moving the goalposts.  You say the dragon does not need to be with you all the time... but also have talked about how it can be used as a mount (which covers large portions of the game during travel) and could shapeshift to increase the amount of time it is with you.  You keep using phrases conclusively assuming that they solve problems, but do not really explain why they solve problems, or otherwise do not respond to problems raised.  For example, in your response to "blurring the line between an DM's NPC and a player's mechanics causes problems" you counter with suggesting blurring this line by having it be DM controlled, but the player can direct it.  You ignore the "wait, are you enslaving an intelligent creature by saying "this works just like command."  You make conclusory statements about power levels that do not seem based in data, just your personal conjecture, and do not acknowledge scaling over time.  One can go through your posts and not find a clear idea of what you actually want - just a series of defensive postures that fail to adequately address the many concerns raised on this thread.

You say you want to discuss in good faith - that means you need to actually respond to counterarguments, not insult others' posts with dismissive "You're just wrong" comments, and be willing to admit you might be wrong on some points.  I have seen lots of good faith attempts to explain the myriad issues in this idea, but not much in the way of good faith responding.  Perhaps work on that a little.

But, ultimately, I think it comes down to the fact you clearly think this is a good idea and everyone who disagrees with you - both Wizards, who has repeatedly gone for near-dragon riders, and the majority of folks on this thread - are wrong.  That is fine. This is D&D and you can homebrew whatever you wish in your game, and I hope you have fun with it.

But I would be surprised if Wizards changes their course.  For all the reasons stated on this thread, it is not a great idea for the general game, with problems ranging from power to flavor to morality to mechanics.