A better damage system isn't difficult...
In my last game (5th edition D&D), we homebrewed a system where we had two HP pools.
One for your shallow bruising type HP. Most damage take from this pool first by default. This pool healed quickly on its own (100% with a full day of rest), but couldn't be helped much by magical healing.
One for vital wounds, where you're really getting seriously hurt. Take from this pool after the other one is gone, or on critical hits (which applied directly to this pool instead of doing extra damage)
On every hit to this pool, the DM would (usually unless game circumstances pre-determined something specific) roll to see which body part was effected and assign a disability associated with it.
Each critical wound was recorded separately, and the disability would remain until it was healed. Critical wounds would heal very slowly, and would usually require healing checks to heal correctly. This is what magical healing (which was limited compared to vanilla) would be for, and would still require heal checks and most likely some time.
The first pool is supposed to represent your fatigue. The idea being that a seasoned warrior learns through experience how to position and move themselves such that harm is minimized; rolling with punches and the like. As you level, you get better at doing this, and combined with the general energy and hardiness represented by your constitution determines how long you can keep it up. But once you're worn down to a certain point, you just don't have it in you anymore to protect yourself properly, and you start taking blows full force. And critical hits just represent especially cruel blows that get past your defenses, regardless of how fresh you are.
Honestly nothing too original. There are other systems that do stuff like this. We just shoe-horned it into D&D with the specific flavor we were going for, and it worked out pretty well. A bit more book-keeping, but nothing too cumbersome. I was playing a Necromancer/Ranger with lots of healing skill, and designed a Mold Flesh (guess what that did) cantrip for myself, so I got to perform lots of dramatic surgeries and stuff. Had to weather a couple interesting situations with one eye blinded and a shattered shoulder. Good stuff.
The best thing about it, besides making HP feel like less of an absurd abstraction, was it changed the problem games like D&D tend to have with the healing role. Where a healer character doesn't do much other than act as a backup group HP pool that everyone draws from during combat, and the role is not only boring to play but has a disproportionate effect on the pace and length of combat.