It's something, at least. It's a lot like the lingering wounds option, in that it uses an extra level of complexity to handle something that just resolved itself naturally under previous rulesets. People who want damage to represent physical injury aren't exactly happy with that implementation, either, but it's something.
It doesn't change the fact that a PC in 5E (or really, any individual creature) is far weaker under Bounded Accuracy than they've been under previous rulesets, but it goes part of the way toward addressing one aspect of that weakness. I'll definitely add it to my list of options to consider, for the next game I run.
I can't stand the lingering injuries option in the DMG because it has the same problem as all other systems that use a table like that. Statistically speaking, every PC will eventually be missing an eye, foot and arm.
I use a relatively simple system.
Critical Hit
When you roll a natural 20 on an attack roll, you score a critical hit, and you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together. Then add any relevant modifiers as normal.
In addition, the target must make a Constitution saving throw (DC 10 + attack modifier). Failure indicates they are staggered. The target can make another Constitution saving throw at the end of its turn to end the condition on a success.
If the target fails their saving throw by more than 5, they are staggered and injured.
Staggered
· You can’t take bonus actions or reactions
· You have disadvantage on attack rolls and ability checks.
Injured
You are staggered (recovered normally) and suffer 1 level of exhaustion. Injuries often leave scars.
You make one death save daily to recover from the injury.
3 Successes: Regain one level of exhaustion
3 Failures: Lose one level of exhaustion.
The first time this failure would cause death, it causes a permanent effect instead (such as reduction in speed, a penalty to attacks with that arm, etc.) instead.
You die if you fail another three deadly condition saving throws.
It uses existing mechanics, maintains an abstract approach to damage, provides a short-term effect that's meaningful in the existing combat (important when you score a critical hit against a monster), and a potential for a long term effect that has significant consequences.