If you change it to more of a hit point pool/quest model, now you're moving back into 70s-era D&D territory, where in-dungeon resting and recovery was very much an exception. Hit point pools are strictly a "per delve" resource. If you run out, you die.
The "lifetime hit point pool" has a bit of an analog in the Call of Cthulhu sanity system wherein your investigator slowly depletes their sanity reserves and goes irrevocably mad. Sanity awards and recovery are, in my experience, usually insufficient to mitigate the losses so the end is a foregone conclusion. That's part of the appeal of the CoC genre. You play to find out what terrible fate befalls your character. However, the sanity system doesn't replace the hit point system, so death in any particular encounter is also possible (or even likely). It adds immediate suspense while the sanity track adds impending doom.
I would consider trying the "lifetime hit point pool" system only with the understanding that:
1. It would be for an adventure or mini-campaign. I wouldn't attempt to use it with the expectation of 1-20 or even 1-10 level of play.
2. The tone of the adventure, setting and game reflected what it does. A story in which the PCs' luck is actually running out and they are on some sort of critical timer. Ideally, it would be set up to accentuate the expected lack of resources towards the later stages of the game.
3. I would probably random generate the PCs' pools in secret. That would add suspense to how much luck they actually have left.
4. Replacement PCs don't get the full complement of hp, but some lesser amount based on the expecting time remaining in the campaign. Or possibly don't allow replacement PCs. You have one PC and one stack of hit points. Good luck, brave adventurer!
5. I wrote the adventure content in such a way to accommodate the system. This would probably include additional traps and random encounters designed to sap hit points.
5. This would require a great sales pitch to my players.
Given all that, I still probably wouldn't bother with the system as I don't think it would lead to fun gameplay. Consequences early in the game, such as losing 100hp in a fight, won't be felt until many sessions later.
What's worse, if you have very careful players, they might not feel any tension in the game AT ALL. If they studiously avoid dangers, they could end their run with the bulk of their hit points remaining. They will end the game either never feeling challenged or never engaging with the adventure.
That doesn't match my value system as a player or DM. I prefer systems or encounters were something is at stake. Consequences are felt immediately and occur naturally from the situation and the responses of the PCs. Any particular encounter might be deadly to the PCs, but they can mostly mitigate these risks with clever ideas, bold actions or, failing that, plain old luck.
Any system that is too harsh ("fail and you're dead!") usually means the players won't engage with the game. They won't take any chances and be paranoid about everything. I find that dull. I prefer to give them a bit of rope and see what they do with it...
Any system that's too lenient ("lose 20hp, which you won't feel for another 6 games") means that the players won't be engaged with the game (care about the consequences). At that point, why bother?