I think the actual application of 'shooting on the move' is different for the combat soldier, and the civilian carrier. This kind of leads to some ambiguity as to the uselfullness of the tactic, as demonstrated by Mr.Howe.
For a soldier in a combat situation, when under fire it would seem much more prudent to move as quickly as possible to the nearest cover before returning fire. Your opponents have indentified you as a armed enemy threat, and are actively engaging you with what is probably automatic weapons fire within the context of a military engagement. Slowing your movement for any reason will only place you in greater danger. Your opponent knows from the start of the encounter that you are a deadly threat and reacts accordingly.
For a civilian in a self defense situation it's different. Your opponent does not initially see you as a deadly threat. Your opponent is a criminal who has picked you, the victim, for any number of reasons, but most of all because he see's you as a 'non-threat' who will offer very little, if any, resistance. He/they do not expect or desire armed resistance from you, nor do they desire a gunfight. They would almost certainly not have targeted you in the first place if they thought that would be the probable outcome. This is were, I think, 'shooting on the move' offers an advantage, primarily as a shock tactic within the parameters of a civilian self defense encounter. Instead of being a relenting victim, you the shooter are now aggressively and actively engaging your attacker, catching him off guard by momentarily reversing roles and making HIM the victim. If this buys you a couple seconds to effectively get good hits on your opponent before he can react, then the tactic is sound. Even if you are wounded in the process but win, it is still sound, or at the very least worth exploring.
Alot of the training schools that now espouse this tactic cater both to civilians, LE, and the military, and seem to have made it be a blanket tactic for both civilian SD scenarios, as well as military combat situations. Thats were, as Mr. Howe alludes to, it kind of rings hollow. There two very different kinds of confrontation. For the civilian in a SD situation, though, I think 'shooting on the move' is a usefull skill and tactic to have. However, if as a civilian in a SD scenario you have been indentified from the start as a deadly threat by your opponent and are taking rounds, the usefullness of it quickly becomes nill... I'd be high tailing it for cover like Mr. Howe!
Just my OP, recognizing the fact that I've never been shot at and don't know jack.