I understand and appreciate your apprehension. However, I can assure you major fractures of the skull will meet this threshold. Instead of a broken jaw, you could easily have a broken orbital bone and loss of an eye. He could also easily sustain a severe concussion with loss of mental faculties.i dunno, it would be for the jury to decide if two broken jaws bones constitutes "serious bodily injury." but i'm seriously guessing not. and i wouldn't want to gamble on it. my mind goes to irreparable life changing injuries under those words. the argument could be however: "without the gun he would've done even more damage" which is likely a very valid argument as the perception of that after seeing a guys face pummeled multiple time is real and likely valid.
i mean, yes, if was carrying a gun and i saw this going down i would probably have it in my hands. as more of a method of "something needs to stop this (in the sense that a loaded gun pointed at an aggressor should be able to freeze up the situation)" vs. "time to blow someone apart" thing.
people get their jaws broken in bar fights over women though, not sure that's a good reason to shoot someone in the chest. but it's also an endless "what if" game that's impossible to play.
If a guy was getting the boots put to him on the ground, and bleeding from the head, would a reasonable person feel there is a likelihood they victim was in danger of or experiencing serious bodily harm?