I'm less convinced about the power/balance issue.
The power issue comes up in a slightly more nuanced way than the' team has an optimal play that they then will always use' boring combat problem. Most commonly the abuses and breaks that arise from being able to move yourself in the initiative order are to do with spell and ability timing, and getting more value for them than intended. Here's an example:
I'm a monk, and there's a big bad in front of me. The turn order goes: Monk, BBEG, Fighter, Barb, Wizard.
I hit the Big bad and stun him. Huzzah. He's now stunned until the *end of my next turn*, giving everyone one round to wail on him, and have advantage on things or to have him auto-fail some types of saves.
Everyone else takes their turns, and then it's me again; "I delay my turn until after Wizard!" Now everyone gets a SECOND full round of that stun, and the BBEG can't do anything about it, and has to skip a *second* turn, because it still hasn't been the end of my next turn because I ducked to delay until after him. And it's cost zero extra resources.
There are other examples as well, but most of them are to do with the timing and duration of spells and class abilities that are balanced around being active for a specific amount of time, metered by the initiative order. Begin able to change it at will, round to round, does a lot more than people realise at first glance.
