Do you think you could elaborate on your complaints with the whole idea of hit points a bit more? You say it has problems, is basic and that it's overused, but that's not much to go on (someone could say that about any commonly used aspect of video games - graphics, sounds, etc.). It seems like you're unhappy with the way most games have the player being able to perform the same stuff whether they're perfectly healthy or almost dead, but is that it?
Sure, fair point. Some of my issues with hit points is the zero penalty until dead. That tends to annoy me most with RPGs. For example a game with casters that have to be protected, it's a fairly standard tactic to just run past the frontline units and just whack the back ones. They'll have enough HP that they can easily take an attack from another warrior class in exchange for killing the casters. Granted this can also be construed as a failure in the RPG to have a steep enough penalty for not facing an opponent / moving past an opponent. But instead, most games have aggro systems and aggro abilities like Taunt as a way to try to protect the caster characters, instead of allowing positioning to actually work. (JRPGs tend to just cheat and let the back row not get hit)
It's also used as artificial gating too often. Just up the hit points on the bad guys, now it's more difficult. (or reduce the damage done by the player) Nothing breaks realism for me like playing a WWII game, and having to put round after round into a bad guy's skull. And Destiny with it's bosses that are basically giant slow moving sponges for damage are really lazy design.
I also hate the clutter of displaying a health bar and/or hit points on every character, and the change in focus that games with hit points and health bars have. You end up playing the watch the health bar game and the try to make the damage numbers get bigger game. Borderlands for example, I'm not really convinced it needs to have the RPG trappings that it does. It could have procedurally generated guns with different characteristics, and scrap the levels and hitpoint scaling, and it would be just as much fun, perhaps more so, as you'd never out level content accidentally or encounter something over your level, or get stuck not being able to play with a friend because the level spread is too great between the two of you.
There are definitely places where degradation of character traits is detrimental to gameplay. Mario is a good example, in that you certainly couldn't reduce the jump amount. However, they do shrink you and take away your fireball throwing ability if you get hit, which is certainly more interesting than if they just gave a HP bar over mario or gave him little heart icons in the upper left.
RE: Sir Weeble: Plenty of fast games don't have hit points. Sonic, Mario both don't have traditional hit point systems.
And I agree everything is a hit point system. Even mario's system is hit points, but it doesn't mean we all have to use the same exact implementation of hit points that we see from RPGs. I want to see more creativity, and more reflection on why someone chooses to use the standard hit point system, and see if maybe they can use something else, or put a different spin on it. I agree we have to be careful not to make a system that is too complicated to grok easily, but I'm kind of tired of seeing large numbers fly out of everything I shoot in action games.