Wouldn't it make sense for a monk to be able to use its normal attacks, plus flurry of blows, when doing a simple ranged attack? Like attacking with daggers. Throwing two daggers, one in each hand, as the normal attack, the grabbing two more from your belt to throw. Perhaps make a high dexterity, 17+ to be able to do this. With the speed of attack a monk is capable of, it makes sense it would be rather easy for them to do. Just weapons easily grabbed and used. Any thoughts?

I think the flavor of the unarmed flurry attack is that the monk makes their regular weapon attack, and then follows it up with an incredibility quick sort of opportunistic punch or kick-- it's not them just taking the time to make another regular-speed weapon attack. To throw extra daggers, the monk would have to draw, hold correctly,  aim, throw, follow through,  control breathing, etc, wheras their unarmed attacks are a function of their ki and its connection to their body. In order to do the flurry attack they allow their ki to flow through them and act instinctively, which allows them to attack impossibly quickly for a short time. 

That's my reading of the flavor of the mechanics. If you want a straighter answer, the mechanics simply state it cannot be done. If you want a ranged flurry attack, play Sun Soul.

Also perhaps, to answer more broadly to the headline of your topic.

I'm guessing the attacks are unarmed to balance the fact that the monk can make two extra attacks at 2nd level, or 4 at 5th level when he gains an extra attack.
To balance it out they made it so you have to use the unarmed attack and damage. Of course in your example daggers deal the same amount of damage as the lowest level unarmed attacks but if you were able to use say quarterstaff you could make three d8+dex mod damage strikes at 2nd level or 4 at 5th.
I sometimes miss the flurry of blows of the previous editions where the monk gained much more attacks as the levels went up (in those editions you could also use weapons with fob)
and sometimes wonder if it would unbalance the monk horribly unfairly to give an extra attack or two at higher levels. Or perhaps allow the monk to sacrifice his entire movement or reaction add an additional strike(in previous editions flurry of blows was a full-round action, you couldn't do much more than that), or perhaps if that would happen the damage input should be diminished.
Also here my old memory does me and 5e a disservice. My first thought still often is that one extra attack for a price of a ki point is a bit steep but that's mostly because
in older editions ki points, much like spells were only recovered after a long rest.

As for your question would it make sense. 5e simplified combat alot from previous editions and mostly in ways I wholeheartedly agree, but they did cut off a few things that made sense, either completely or in a way that you can get them as a feat. For instance it used to be so that if a prone opponent got up in front of you you got an attack of opportunity.
Thats gone. Or if a spellcaster attempted to cast a spell in front of you you got an attack of opportunity to attempt to disrupt them (not sure about the touch-attack spells but otherwise)... that you can get from a feat. Those two attacks of opportunity make sense to me, if you still have your reaction to spend that is, and I don't really understand why they took them away.

As for your suggestion about making what you propose a high dexterity check... I think that too has to do with simplifying the mechanics. In previous editions there were a plethora of interesting battle(and sometimes otherwise) mechanics about different stuff in different situations, it could sometimes be cool but it also could sometimes be really frustrating.
and it made the learning curve to the game steeper. So to make such rulings "you can do this and this only if you have this and this number in these stats" might add unnecessary complexity to a beginner
Of course one of the great things about the simplicity of 5e is that you can house rule and homebrew stuff or possibly even import ideas from previous editions (in that case you may need to modify them as those ideas sometimes contain things about game mechanics that don't exist anymore).
If you're in a game talk it over with your dm

Perhaps, under the new rules, I should have said make a Dexterity skill roll in order to do this, and if it fails they drop the daggers. What made me think of this was I had a friend in to martial arts years ago. He had an outfit which had two pockets at the top of of th shoulder blades. He told me he could have two throwing weapons in his hands, then easily reach and throw two more in the same motion. Obviously, this could only be done once, at the beginning of combat. I never saw him do this, but he went to Japan, Korea and Nepal to study for a few years. 

I do miss some of the old rules as I had, and still have, a monk, who eventually made it to 20th level after 6 years (though he gained nothing after 17th). He had the finger of death, healing and psionic abilities, along with exceptional strength (no bonuses allowed for "to hit" or damage, rolled by a TSR rep).  Rolling 8d4 dice for every hit perhaps was a bit much under the old rules, but you only had 72 hit points max. If it weren't for magic items available in 1st edition lower level campaigns, it never would have made it to that level. When I stopped playing, he had a monsatery, castle, a small walled city, mining operations, and the high level magic users and clerics he employed made many common magic items. A LOT of phone calls to TSR about what was allowed, were made. Wish I could have imported all of this in to D&D Beyond, but as for now, I am reproducing the maps, PC's, etc. from my old records. 

Sounds like an awesome campaign. =D 
Yeah I miss some of the old stuff too. But I have to admit 5e has done alot to fix the monks multiple atribute dependancy and made it more playable anyway, you no longer have to take a feat to be able to use dexterity to hit (now you can even use dex to damage which is great), I made a list in a different discussion of many of the improvements:
The ki point restoration after a short rest is great.
Slow fall is better, you no longer have to be touching a wall.
The immunity to poison and disease including the damage is great. 
just having to take an action to rid yourself of being charmed or frightened is also pretty dope, still mind before only gave +2 bonus to saving throws against those.
Tongue of sun and moon is better, if only because it comes earlier so you can enjoy its benefit longer in the campaign. Not just a few last levels.
Losing the quivering palm as a class ability to simply one of the sub classes is a bit of a bummer but then again the
open palms quivering palm is way more applicable.
Timeless body, with its addition that you no longer need food or water is better, before it was only good if you played a long enough campaign to have your character become so old
you'd get age penalties.
Diamond souls addition to be able to reroll failed saves with ki point makes it better I think.

Not sure if the 20th level perfect self was better or worse, but it wasn't anything super special to write home about before.
A later alternative to the perfect self "Old Master" which gave a bonus attack and a +2 to AC is clearly better in the old version
but thats neither here nor there. And at that point it might be a bit late anyway. That extra armor could've been used earlier.
Unless you plan to play alot of campaigns starting at 20th level its not really that big of an advocation to either version.

Edit: okay the +1 natural armor every four levels in previous eds or atleast Pathfinder was pretty nice, but I'm pretty sure back then combinations of other armors wielded by other classes could also rise to same level, or even above it pretty fast. You still needed like 18-20: 4-5 to
Dex and Wis for defense, the nat ac had to be in pretty high levels before it might make any difference
 
I think 5e did alot of great stuff to improve the monk from the mess of interesting but badly implemented ideas it was before.
Sure I too think it could be better, perhaps since Wisdom is no longer tied to how many ki points you get the additional stat for armor could be
Constitution to complement monks poor hit die.
Or perhaps the monks could use dexterity instead of strength when grappling/performing other combat maneuvers (actually grapple and shove are the only cms left)
It wouldn't necessarily be that weird of an idea. While strength is important in grappling combat how fast you can go for a grapple or attempt to change a situation in a grapple, namely speed is also very important. I practiced a bit of martial arts younger and I remember alot of smaller and weaker guys, and occasionally girls dominating me in grapples even on the ground simply because they were faster. This might go a bit further with eliminating the M.A.Dness of monks.
Sometimes I think that maybe an extra attack could be added to the flurry of blows. While it certainly doesn't need to be the seven(?) attacks of the previous editions
I sometimes wonder if one extra for the price of a ki point is a good enough trade, though the fact the monk can move unlike previously while doing the flurry is a great addition and does balance it out alot.
In many ways it is balanced pretty well and I really like what they've done.

lets hope that at some point some of that old cool stuff you mentioned can be imported here :)