Most abilities should be either “per round/turn” or “per encounter”.
Abilities that are too powerful for that should either not exist or require significant preparation (enough for the opposition to have a chance to discover and interrupt it).
Abilities that fall in the second category should automatically come with a less powerful variant in the first category.
Maybe as a middle ground some player abilities could use the “roll for recharge” mechanic from powerful monster abilities.
I kinda disagree with all of this. Big abilities that come with in-universe complications are the bread and butter of RPGs. E.G. Connection: Mafia: You know a guy in the mafia you can ask for help, but he might want a favor later…
Or think of things like Wish, etc.
It kinda sounds like you want a wargame with a bit of story connecting the battles. Which is fine, but then just play a wargame I guess?
I think we don’t actually disagree and I was just not precise enough in my original post.
What I described above applies to abilities that are relevant in combat and any other type of encounter that the respective system mechanically treats as a conflict similar to combat. That absolutely does not mean other abilities should not exist, just that they should not be practically usable during an ongoing combat-like short term conflict.
Also: Abilities that are useful in short term combat-like conflicts and abilities that are not should not compete for mechanical resources of any kind, that is never fun.