You can't always keep your weapon hand (or both hands for that matter) free. I have 2 small kids. One needs to be carried and the other needs his hand held when walking through the parking lot for example. When a person is distracted by their children they become an easier target for any unsavory characters in the area. You can bet I'm not going to drop my daughter on the asphalt to draw my pistol, nor am I going to find it acceptable to let go of my 3 year old son's hand to do the same in many cases.
In order to combat that sort of two way bind situation, I've been working on teaching my son to hold onto my pocket or belt loop rather than my hand, but he's 3 ... he's more easily distracted than I am, so it's not as easy as all that.
As far as the military training you to "keep your strong hand free" that's a new one on me and I spent several years in the military (U.S. Army; Ft. Jackson, Ft. Benning, Ft. Campbell). As far as needing your RIGHT hand free in order to salute at a moment's notice - maybe in training... There are SOPs for saluting, and "at the drop of a hat" isn't exactly one of them
Personally I carry more than one defensive tool - a gun, a couple knives, and keys with a stout steel keyring. Depending on the circumstances of the situation, a person might not have time to get a hand on a weapon even if their hands are both empty. Yeah, it really does happen that fast, even if the assailant is 20 feet away - If the attacker is any good at what he does, you likely won't even notice him/her until it's much too late.
In other words - get training, practice the skills you learn, get more training, be aware of your surroundings, and live your life - don't over think the self defense aspects of life or you're liable to not only miss out on life itself, but you could be too busy LOOKING for threats that you miss the obvious one right in front of you.