Yes it is. You are threatening death or severe injury to the other guy.
Since the number one objective in self defense should be to get away from the attacker.
I do admit that my theory breaks down when talking about store owners in inner cities. THey I do feel have a legitimate need for firearms.
Wrong. The number one objective in self defense is your own safety/survival.
Running away is not a very good solution, because you have no idea if they can run faster than you. If you're woman wearing high heels facing a potential rapist, you will not outrun him. As for in your own home, absolutely you have no cause to run away, besides, depending on where you live, you might not have an escape option behind you. Hold your ground, you have them in visual contact, there's no chase, there's no "oh god where is he?", just shoot him and be done with it.
Your theory doesn't just break down, it never was viable in the first place.