There's also a meta-game issue, where it feels like the player is being punished by having to play a broken character, when they would be allowed to bring in a healthy new character if the first character had actually died. You can solve that by requiring any new character to enter the game at a lower level (or whatever) than the old character, but the disparity has to be pretty significant for the player to actually appreciate being broken rather than dying entirely, and that can feel like a no-win situation.
We let people retire injured characters if they wished, but new PCs came in with 2/3 avg party XP so they usually came in 1-2 levels down and stayed behind a while.
We also generally were more of a gritty group so scars and missing eyes and fingers were things that showed your character's experience and his ability to survive bad things. We had one character get a dwarf-made multi-socket for his missing hand - he could snap in a sword, axe, hammer, a primitive gripper, a spring loaded dagger, or some other bits. Sometimes he just used a huge fist as his second weapon.
And when people had gargoyle claw furrows on their heads, the locals knew they were tough and didn't usually give them much fuss. (I think we gave increased intimidation mods for some serious scarring).
It also applied to NPCs, repeat villains, and foes. So if you broke a major foes' arm, that meant you were more able to take him down.
The truth is some of the middle level PCs (our party was usually scattered over 4 levels from lowest to highest at any given time) and that didn't matter. Generally, how smart you played and how well you could figure out what the enemy du jour was up to was more critical than your stats. Sure, the strongest fighter could stand the longest and take the biggest hits, but he didn't advance the larger picture as often as the rogue or the mage.
Aside: Not game breaking, but hilarious -> One of our Champions PCs who had a public identity as a super successful athlete / hero decided at one point he had a few points to spend and got the insane notion to buy "Faster-Than-Light Travel, usable only in a vacuum' along with some other strictures so it was pretty cheap. Now, we were not playing a star hopping game. We were city bound. The PC had no flight or life support. When asked why, he smiled like the Cheshire Cat and said "Lance fast!". (lol!)
I once played a tactical space combat ruleset called Red Chicken Rising (I am not making that up). It was the only wargame rules to date to begin with a shower scene I believe. It was a bit tongue and cheek but played okay. However, that was if you used the standard pre-designed ships. They had beam weapons, shields, and boarding parties (some of each). When one of our guys looked at the build system, the designers had made thrust and boarding parties pretty cheap (vs. guns and shields) and most of the time, boarding didn't happen.... unless you designed custom large ships with LOTS of thrust and LOTS of boarding parties and nothing else. Then your fast moving boarding torpedo with a batttalion embarked that could be purchased for half the cost of a cruiser made for a game breaker. "Hi, we're taking your ship. Resistance is futile."