I mean, to be fair, getting shot requires surgery anyway if you start bleeding because you have to remove shrapnel because internal bleeding. That means that this suggestion for getting shot is already in effect. Not a fan of falling over helpless though. If you've lost enough blood to fall over, then you're either in pain crit or soon to be dead because you're already on the floor taking massive oxy damage. Basically, what I'm trying to say is that it already exists, and that we don't have to make it worse as this suggestion would make it
Coupled with that:
Surgery uses a cautery to close wounds. No need for sowing and bandaging.
Also, there's already a bleed system in effect anyhow. Being attacked with things like knives, claws, etc. makes wounds tear open which cause bleeding. The bigger the wound (due to repeat hits), the more you bleed out of said wound. The smallest of bleeding wounds will heal naturally, but bigger wounds require gauze/advanced trauma kits to stop the bleeding.