I wouldn't. But because of the relatively slim chances of me needing to protect my wife and son I would rather rely on my wits than deal with the burden of carrying a weapon on me at all times.
These situations are very scary, but I lean toward what you said here. If I don't have a gun, and something happens, I am "all in" with regard to trying to think my way out and focus on escape.
If I have a gun, would I hesitate? Would I think to find a tactical position instead of escape? Would I think my chances were better to find a tactical position and try and survive that way?
I don't know, but I do know that once I draw my gun or am about to draw it, then I am all but committed to a firefight. I think winning a firefight is very difficult and even if you manage to actually hit the person, you can still get shot so easily. In this case, the guy didn't even get a shot off.
In a situation like this, my shit would have bolted.
In a gun fight, I have no reason to think I would win against even the most average criminal. Even with training and practice, the unpredictable nature of these situations, as well as difficulty in aiming a hand gun under pressure, makes me think my chances of getting shot are pretty damn good.
And don't troll me about not being able to aim a hand gun. I've seen videos of cops unload a whole mag at a stationary target and completely miss. Under pressure, pistol accuracy sucks unless you are damn good, as in way, way above average.