Don't think it's a dumb idea at all! Hit points have always felt more like a measure of how lucky/important the characters were to escape death, since you only start to die when you run out of hitpoints, literally running out of luck. But just relying on that alone will probably still not be enough because some injuries would be too obviously bad to ignore. The fiction of just 1000HP that never heals is not very evocative for D&D (though I can imagine a game where this system would be amazing fun!), so I think the core idea of managing hit points should still stay.
I would think that a system that has the most "verisimilitude" when it comes to injury and death would be a mix of Plot Armour points and injuries. If using D&D and you want a more "sim-like" experience, you could potentially homebrew a system that uses components the game already has. Something like this:
1. Hit points are your Plot armour points. They can no longer be healed by everything, but they will always recharge to full after a long rest. Hit dice now represent recharging your luck.
[Note: While I think it would be more evocative if no spells can heal hit points, I imagine some abilities or spells might be better flavoured if it heals Hitpoints instead, e.g., Bards.]
2. When rolling for damage and inflict the hitpoint damage. Then, at the end of turn, inflict the corresponding wound as exhaustion based on the total damage received:
2a. <10: No wounds
2b. 10-19: Minor wound, 1 point of exhaustion for every 2 incurred
2c. 20-29: Moderate wound, 1 point of exhaustion
2d. 30-39: Major wound, 2 points of exhaustion
2e. 40-49: Deadly wound, 2 points of exahustion and roll death saving throw.
2f. 50+: Lethal, 2 points of exhaustion, auto-fail death saving throw.
[Note: I am basing this on monsters expected DPR. At around CR3 is when monsters start dealing about 14-17 dmg per round (roughly), which feels about the right point when wounds can be introduced to players and they start wounding them.]
3. Track the wounds, maybe with a simple symbol that fills the exhaustion track: strikeline for minor, X for moderate, and fill out for major and deadly. Spells that usually heal hitpoints now heal these wounds. Low level spells heal Minor wounds while higher-level spells heal major/deadly wounds.
[Some tables might want to only apply the exhaustion penalties and death saving fails at the end of combat rather than during.]
4. Rules for exhaustion still apply. But if it feels too much a table could double the exhaustion track (so 12 pips instead of 6; the exhaustion penalties trigger at every second filled pip) to give players a bit more breathing room.
5. The armor worn now also helps to reduce the level of wounds. Light armor adds nothing; medium armor reduces the wound tier by 1, while heavy armor reduces the wound tier by 2. Now the heavier armors will be even more important. Class abilities that affect AC (Monk, Barbarian, Dragon Sorcerer) will be treated as having medium armor.
6. Play proceeds as normal. Once your hitpoints run out, your luck runs out, every successful hit is now at minimum a moderate wound and your death saving throws still apply.
I think this system would address some of the issues people have with 'realism'. Being stuck in an Acid pool probably inflicts at least Major wounds every round, so pair that with hit points to give palyers a reason to want to get out quick.
For this design I am using the vibe of Stark and Fern from Frieren in their first real fight against demons. Stark's battle would be beautifully modelled with this system; taking hit after hit and becoming badly injured, but still managing to pull a win at the end.
---
I only now realise that I spent a lot more thought on wounds rather than the hitpoints as plot armour points itself. Haha. But then hitpoints have always been a very stable concept and doesn't really require much change; it's the concept of injury and how to represent it more grittily that's been the challenge for D&D games.