If I just shot someone the last thing I would do is try to render first aid to the man. One moment you are “in fear for your life” and two minutes later you are deciding that this upstanding person is worthy of your first aid? What message is that going to send to a DA or a jury?
A lot would depend upon the nature of the thread and the effect of the bullet. The legitimate purpose of shooting someone in self-defense is to neutralize the threat. If that happens to kill the person, fine, but the purpose is supposed to be to stop the attacker.
In many scenarios, I would not expect that someone who had just shot someone else would be inclined to give first aid, but I would expect in other scenarios (e.g. if one knows that the attacker is generally a good person but has 'snapped' for some reason) one might be forced to use deadly force to stop the attacker, and yet not particularly want the attacker dead. Killing the attacker would be preferable to not stopping the attack, but if the attack can be stopped with the attacker surviving that may be preferable still.
“What message is that going to send to a DA or a jury?”
If you let a person whom you injured die by not at least calling 911 they’ll charge you with murder.
I saw a case on tv (real, not scripted) where what would have been a good shoot turned into murder because the citizen let the guy bleed out on his porch. The video camera the citizen set up to document the dead guy’s recurrent violent behavior got it all.