Homebrew Rule to speed up combat

Hi everyone, 

I saw an idea on social media where you can speed up combat by having the players all go at once then have the npcs go. I see how it would speed up combat. I am wanting to implement it but not sure how it would work. Here are some things I have been considering. Feel free to give me ideas, suggestions, etc...

- Have everyone still roll initiative. But if the NPC rolls higher than one of the players, they are able to act before that player. 

- This could open up combos the players could perform. I could reward with extra damage. 

- One difficulty is I would have to sacrifice a bit of realism and go by instinct. This would mean the players would have to abide by my rulings. I could consider their explanations as well. 

- I would have to get into the head of the NPCs. DMs do that anyway right?

Let me know your thoughts.

I've run an asynchronous game like this. Things to note:

1. Yes players can pull off some combos that would be very difficult otherwise. You DO NOT need to award any bonuses to this, the power of the combo is its own reward. Instead you will need to add additional difficulty to the combats for them to feel like a challenge -> especially having enemies with stronger incapacitation effects or willing to kill the player characters because dropping a player to 0 hp does very little in this style of game because another player can heal them at the start of the player turn and then the player gets a their character's turn as normal. Alternatively use additional HB rules so that a character always loses 1 turn if they are reduced to 0 hp by the enemies.
2. Initiative is irrelevant, don't roll it, it's a waste of time. Instead the first round of combat should always start with the most powerful enemy(s) - unless the party successfully surprise the enemies - then the player characters, then any minions or low power enemies. This ensures your Big Bads always get at least one turn rather than all the players dog piling them and obliterating them before they get to act.
3. I don't know what you are talking about with respect to realism?? D&D combat is already extremely far away from realism.
4. The point of this system is so that players who know what they want to do can act while the more uncertain players are thinking. So ensure your players understand that everyone waiting on someone else will not be acceptable, and those ready to act should act immediately even if it isn't necessarily completely optimal.

No matter how you do it, it still comes down to the players to speed it up.  Players need to know when they go/roll. Players need to know what they will actually do, and need to know what is allowed or not.

Combat grounds to a halt when a player does not realize it is their turn and/or don't know what they are going to do. 

Having 'side' initiative, in any challenging encounter, tends to devolve into "all the monsters go at once, pick one character to dogpile, and kill them before anyone can do anything to save them"

Quote from Pantagruel666 >>

Having 'side' initiative, in any challenging encounter, tends to devolve into "all the monsters go at once, pick one character to dogpile, and kill them before anyone can do anything to save them"

 Only if the DM wants to play it like that.

Which is the case in general. Even with scattered initiative, if the DM wants to have all the enemies focus fire on one PC, it's going to be very bad for that PC very quickly.

Quote from jl8e >>

Which is the case in general. Even with scattered initiative, if the DM wants to have all the enemies focus fire on one PC, it's going to be very bad for that PC very quickly.

Being focus fired is always difficult, but scattered initiative means things like feeding a potion to a downed ally is possible.

The reason legendary actions exist is precisely to avoid having the monster just do all its damage all at once, as that's likely to obliterate a character.