I think the more important balancing is just ‘making battlemaster maneuvers resourceless and available to all classes’.
But I’m not against ‘limit break’ as a short rest ‘charge’ available to most martials.
TBH, the above is basically the way PF2e handles martials; at least half of their class feats are more or less ‘resourceless maneuvers’, and many martials have access to ‘focus spells’, which are basically just short rest charges for exclusive class features, that just happen to mechanically be considered spells (though, notably, PF2e doesn’t give fighter focus spells, making them nearly 100% at-will).
Personally, I think the most important fix to the martial-caster imbalance is to nerf casters, who just are too strong, but A) that’s basically what PF2e already did, and its largely complained about (though I love it). And B) Its not strictly necessary, if you buff Martials by a large margin (though, imo, that starts to get into like, demigod territory that I don’t love).