One of my issues with hit points is this: which of the hit points represent the capacity to absorb wounds, and which of the hit points represent luck, fate, and good fortune? I ponder this issue, because the rules for the recovery of hit points vex me. While wounds should take time to heal, the same may not be true for luck and fate. Admittedly, hit points are an arbitrary and artificial representation of of how much risk you can endure and how battle-proficient you are. But if hit points, particularly at higher levels, are mostly luck and fate, why should it take several days, or weeks, to recover it? What purpose does the slow hit point recovery rule serve, other than to arbitrarily delay the adventure?
WOTC's 4E solution to the problem of hit point recovery is to implement their healing surges system. That allows players to recover hit points after (and sometimes during) combat, thus extending the game day, and shortening the periods between adventures. But WOTC's solution to the recovery of hit points is as arbitrary as their rules for meting out hit points in the first place.
Another of my issues with hit points is a selfish one. As a DM, I find it annoying to track hit points for multiple antagonists, particularly when those antagonists are mooks or rabble. For example, here is a wandering monster table from Module B1, In Search of the Unknown.
As you can see, the hit points for the eight Orcs range from a high of 6 to a low of 2. With the characters inflicting an average weapon damage of 4 on the Orcs, most of the Orcs will be killed with a single blow. But three will need at least two hits to dispatch. Tracking which Orc has how many hit points may not be terribly onerous when there are only 8. What if there are 28? Again, (and for "cinematic effect") WOTC has solved that problem by giving rabble one hit point. You hit the rabble, and it dies. Again, their solution works, but is completely arbitrary, since Troll rabble and Orc rabble both have one hit point.
My preferred solution to those problems: implement a system of wound and luck points, and rationalize and condense hit points to a level where a a hit point equals one successful hit.
With regards wounds and luck, each player would possess both wound points and luck points. When damage was inflicted, a player could chose to use their luck points to avoid the wounds, and the luck points would be refreshed, either after each battle, or after a good night's rest. Only the actual wounds inflicted would require healing.
As for rationalizing hit points, some number of hit points would be condensed into wound and luck points. For example, 3.5 hit points might equal one wound point. Weapons would do one wound, unless they were either exceptional or magical weapons.
The biggest problem I see with this solution: rpgers love rolling dice, and implementing such a system would eliminate the need to roll for damage. No more euphoria when a player rolls the maximum weapon damage, nor the groans of despair and recriminations when the player rolls a "1".
Such a change might be too much for players to bear.