I do not understand the request for faster combat.
Do you not have time to play the game?.
I think in a lot of combat it's not an issue but there are some fights where the AI has issues and there are a lot of enemies. The best example is taking on the Goblin camp courtyard, there are 2-4 adventurers and about 10 or so opponents. Some of the AI here can take about 10-15 seconds to take a turn so if you have characters of similar initiative then you can go a solid 90 seconds just waiting.
If instead those goblins all performed their movement at the same time then attacked in quick succession then ideally you could half that time waiting.
I don't think they should go back to team initiative but I do think it would be good if an AI that has the same initiative and team would perform its movement at the same time when possible [just like players can]. I think they should not all perform their action / bonus action at the same moment but each take it in turns so that the combat is clear to read.
Functionally the enemy would be able to do the same as they already do however it would be more streamlined.
When I'm playing multiplayer games with friends, we do indeed have some time limits. We can save mid-combat and come back if necessary but I think we'd all prefer it if the combat was a bit snappier.