Realistically, there's a few things a character should be able to do at any time, regardless of turn order or anything else:

Because, Realistically, rounds, turns, or initiative orders don't exist, they're abstractions, to
reduce (no, really) complexity...
--- speak (briefly)
--- surrender
--- collapse to the ground as if passing out (or dying)
---also, actually passing out or dying
---interrupt spellcasting
---complain about the lack of verisimilitude inherent in turn-based iniatitive.
Also, the in-combat movement RAW in all the WotC editions turns movement into little mini-teleports: you're here, and now you're there, with no time taken and no chance of running into that lightning bolt that just crossed your path.
TBF, you do pass through the points between, and the whole set of off-turn/initiative actions, OAs, Delay, AoOs, Immediate Actions, Ready, Free Actions, Swift Actions, Reactions, are to
avoid having turn-based initiatives turn into teleportation and freeze-frames.