Hit points certainly are a little odd. But it's not hit points that are my qualm with the system, because in their representative state they do what they're supposed to do.
What gets me is weapons. Sure, you have the opportunity to extend threat ranges, and use Power Attacks, and buff strength... but really, under the basic rules a hit from a first-level fighter isn't going to do much less than a 20th-level fighter with the same sword. (The hit chances are greater, but for thousands of times the experience, you'd think there'd be a little more damage.) That is the real problem.
User skill isn't going to account for much in such a paradigm; endurance becomes the measure of the hero. It's still possible to kill them in their sleep at high levels, but not probable unless you do massive damage yourself in a coup-de-grace. And as has been stated, it's practically impossible to die in one hit.
What you really want to do is increase damage by a heavier margin with experience. Here's one idea that (while probably completely unbalanced and clunky) might give people a way to work around this:
Instead of rolling for damage, just subtract the enemy's AC from your attack roll, multiply by the size of the die you're using, divide by (say) five, and do that much damage. If you roll a threat, roll again and add the new roll (this can continue ad infinitum).
I won't pretend that it's perfect. But does anyone like the idea?