Combat is the easiest thing to bog down in D&D. The D&D combat mechanics are already clunky as hell and the initiative + action economy systems tear at the seams if you put too many creatures acting individually on the initiative tracker. You've probably seen advice to turn lots of enemies into "mobs" that all act as one creature; this is great advice and I recommend it too, but I don't see a lot of advice for what to do with NPC allies.
If I want NPC allies to feel helpful but I don't want to stretch everyone's patience by adding to the initiative tracker, I give the NPCs a different challenge to handle. They're fighting a different mob of enemies in the next room over or in the rafters above, they're trying to translate the ancient text, they're prepping the banishing ritual to blast Mephistopheles back to hell once the players have weakened him enough.
Allies don't act on initiative. A couple times per round I'll narrate something they're doing, just to keep the players apprised and feeling like the NPCs are still there. I'll let the groups talk to each other, but otherwise they don't interact.
It's simple, but works really well. The PCs feel like the NPCs can hold their own so they don't have to look after them all the time, you can get some fun banter going between groups that adds to character development, and best of all combat doesn't take twice as long as normal. It's win-win-win.