Here's my preferred healing system.
Hit Points Represent Fatigue and Scrapes
You have hit points. Getting 'hit' in combat means the attack made contact but didn't necessarily leave a lasting wound. It just wears you out. If you drop to 0 HP, you are helpless but conscious.
Whenever you rest 5 minutes, you get back up to half maximum. If you rest for an hour, you heal to full.
Wounds Impose Penalties
Whenever you suffer a critical hit, instead of taking double damage, you take normal damage and get a wound. There are six possible wounds, and the duration can vary based on how many HP you have left. You'd roll a d6 to determine which wound:
1. Head - Blinded for one round, then everyone has concealment against you as long as the wound lasts.
2,3. Arm - Drop what you're holding, then disadvantage with attacks or checks using that arm as long as the wound lasts.
4,5. Leg - You fall prone, and then are slowed as long as the wound lasts.
6. Chest - You suffer a level of exhaustion as long as the wound lasts.
Wound Severity
If after the critical hit you still have any HP, it's a Light Wound. If after the crit you are at 0 HP, you make a Con save. If you succeed, it's a Serious Wound. If you fail, it's a Critical Wound.
Light wounds heal on their own after an hour's rest.
Serious wounds heal after a day's rest.
Critical wounds never heal on their own.
Cure Wounds spells can fix wounds, though. Cure Light is 1st level, Cure Serious 3rd, Cure Critical 4th. Those don't restore any hit points, though. Nothing restores hit points other than resting, because it's bad game design to have character roles devoted to healing; that's reactive, and generally unfun.
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In this way, PCs will tend to get some light wounds that might change their tactics during combat, but afterward they can rest and heal. If the scenario puts pressure on them, they might rest five minutes to get some HP back, and have to deal with the wound lasting a while.