As I am not very familiar with BM damage potential, I can't really respond too much other than to say while the damage while you have superiority dice would be greater, once you run out my variant should do more I would think? Maybe I am wrong???At will trip attack is also really good - though it taking your bonus action mitigates a lot of the things you could do with it.
Overall - I think you've pretty significantly cut down the high celing damage potential of a battlemaster. You've boosted most of the basic non-feated battlemasters -but overall you'll struggle to keep up with a Paladin or even barbarian in damage now. Heck, it's quite possible that a decently played rogue would out damage this - which feels pretty bad IMO.
Maybe at our table then it would be different. Monks do run out of ki, casters run out of spell points (we stopped using slots a while ago!), and NO ONE at our table plays a BARD!!!shrug I mean you get 4 SD per short rest until 7th, then 5, then 6 at 15th. I don't think you're short of them in most combats. I also don't think they're any more onerous to track than ki points or sorcery points or spell slots or Bardic Inspiration die or any other resource that classes have.
Are you going to re-work all of those as well?
In general, no I am not a fan of limited resource abilities that don't make sense. Tell me, why are the features for BM in the RAW limited? Other than balance, what is the reason? Can I only "trip" foes so many times? Can I only command an ally 4 times until I rest for an HOUR? Is it that exhausting?
Other things, like spell points or slots, even if I don't completely agree with them, I can understand the logic behind them.