I wouldn't remove but re-purpose them, as said before I'd include a blood loss system, hitpoints represent your blood loss. The harder your wounds are the faster your HP ticks down.
It would still count them in % for some things, reaching a certain % of HP/Blood loss severely weakens you, down to 10% you run high risk of passing out. 0% would not necessarily mean death though, that means you KO, if you health ticks all the way down to -20% you bled to death.
This is kinda taken over from how some DnD versions work by not having 0 HP as death but -10 HP, 0 simply means you're disabled from acting and basically a "one hit kill" then.
I do agree that 0 health shouldn't kill me.
If I get "killed" by a citizen/guard, I should be knocked unconcious and taken to prison. It would actually give me a reason to escape prison, and guards could be made hard until the mid levels without my low levels getting killed whenever they steal a spoon.
If I get "killed" by a bandit, I could get captured and enslaved, at which point I'd need to escape from the bandits or whoever I'm sold to.
If I get "killed" by a necromancer, I'd be captured and taken to get rituals performed on me. I'd have to escape, and some good inventive things could be thought of here.
I could even get some quests this way. If I get "killed" by a daedra, I could be taken to the prince/the prince's shrine, where they could offer me to do things for them (I fill some kind of prophecy or something)
If the NPC has no use for me/don't care about giving to the guards, or it's a non sentient creature, I would just be killed after I've got to 0% health. It could add a lot to gameplay.
But, I don't agree that health should be done in percentages.