Just my inclination, but I've found RPG healing to be more akin to video games. It feels like the Cleric is dutifully recharging batteries after every skirmish. In most fantasy fiction, the characters recover quickly from their scrapes and battles, but when they are healed by a cleric it is a miraculous thing.
I would honestly be in favour of allowing characters to recover nearly all lost HPs when they have a chance to breathe after a battle. But when appropriate, give them busted ribs, wrenched joints, or a smashed ruin of a nose. When the cleric calls upon his faith, it feels more significant.
From a rules standpoint, you free up the cleric from his healing duty. You also free up the party from having to have a cleric. This also allows the party to continue w/ fewer camps being made. I suppose cure light wounds would then deal w/ sprains or minor tears. cure moderate wounds could deal w/ broken bones, and cure serious wounds heal life threatening injuries like pneumothorax or a gangrenous limb.