I am not going to change my definition of self defense in order to make fighting skill more important.
People have different roles. Those roles determine what our fighting skills should be accomplishing. As a civilian, your fighting skill should be about surviving and going to work tomorrow. As a LEO, your fighting skill should be about detaining people. In the military, killing people. My assumption is that we are talking about civilian self defense.
I have already pointed out, how you really don't know what the other guy has, until to late. The longer you are engaged in using your fighting skills, the more opportunity you give the other guy to produce anything he has. There is always the lucky shot or weapon of opportunity as well. Your risk for injury goes up, the longer you are engaged.
There are many threads here about the legal aspect of self defense. The take away is that it is not an easy, cut and dry question. If you are in a situation where you need to use your fighting skill, and you get to a point where you could run away and you don't... then you are choosing to stay and engage in combat. That whole complicated legal mess that is self defense, just got a lot more complicated because you choose to continue to engage in combat. A really good bit of evidence that should help your case for self defense, would be that you ran away. You were in fear for your life, or great bodily injury... and you ran away, as soon as you could. This looks better than you were in fear for your life, or great bodily injury, so you engaged in combat, choked him out and or pounded his face to a pulp. The bit where you ran away, supports the statement that you were in fear for your life, much better than ground and pounding him into unconsciousness.
Given the choice, I will use every other skill first, before physical combat. If I have to use physical combat, I will use it to escape, and then escape. If that lowers the importance of fighting skills in self defense... I am okay with that.