I may be an outlier, and don't mean to knock the idea (I support all the homebrewing), but on those rare occasions I get to play, I love to play fighters. The thing is, I wouldn't be excited to play a battle master fighter – certainly lower down on the fighter subclasses I would play – because I enjoy more simplicity. The efforts to 4e-ify / Book of Nine Swords-ify / wizard-ify the fighter class felt really weird to me... if I wanted to be a spellcaster, I'd play a spellcaster. It's the simple yet adaptable part that draws me in.
EDIT: But if you were to implement a fighter-wide superiority dice rule, I wonder about swapping in Hit Dice instead. It's already a resource the player will be tracking or will learn to track, so why not double up on it? Less complexity, no need for another system.