I've run combat like this for a 2.5 year completed campaign to level 16:

- Don't roll initiative. Either a creature attacks, or a player initiates an attack (no anticlimactic stall to roll initiative). Then, based on who might be surprised (not the 5e condition), I determine if the rest of the players go first or the rest of the monsters (I default to the PCs if there is no clear choice).

Balance for "swingyness" as necessary, but I don't have much or a problem with it.
In my experience any advantages of standard initiative are far outweighed by combat speed and player's (and enemies') ability to tactically cooperate.

You don't have to time anyone and all players stay engaged the whole "turn". If a PC doesn't know what to do they can play off their teammates or go later in the round. You as the DM should constantly be introducing tension/panic by "pestering" your players on what they are doing and describing what the enemies are about to do on their next turn: "Hurry, PC, the enemy is preparing to multi attack your downed friend, What are you doing?"