I could see that, sure. I can think of a few...let's say, Vegas-Minded people, who would love it.When things like this have been brought up before I remember being convinced that it really makes the game not fun to have to decide how much closer to death you want to be to do things on a regular basis.
One place I've wondered about using it is when people run out of their daily or short rest abilities. What if you usually only do that maneuver once because it's so taxing... but if you reach down and push it you can do it again. Where reaching down and pushing it is the hit point expenditure. (I could also see exhaustion instead of hit points too).
Having exhaustion points could work too, though it's an additional resource to track; I figured hp makes it simpler. Or maybe the first manuever in a battle is free, as you say, and then it costs. There's lots of room to tweak. The advantage, though, is that we could get some really neat scaling maneuvers without it being "but that's just spells" or "Why doesn't she do this all the time?"