Are you going to get close enough to apply first aid to your assailant?
I'd like to think so - assuming the threat is over.
The goal of self defense is to stop the threat, not to kill, plus, I don't like to think of myself as the kind of person that would stand by and watch someone bleed out - even if they had tried to take my stuff. But, that's less about them than it is about me.
I absolutely agree that everyone should have at least basic first aid training. As a group of people that tend to take some time preparing for the worst it does seem like most gun owners would make that choice. After all, you're far more likely to need to take advantage of first aid training than self defense training.