"WHAT COVER?! Let's face it: If you have to draw you will be suprised and cornered or at least close to the threat. And no glass, car body, wood door or diner-table etc will give you cover from a 9x19mm or a .357 Mag."
True. There is precious little cover with those barriers. But there is concealment, and that is almost as good. It still tilts the odds in your favor, and is sure better than nothing, even it all it is doing is preventing the BG's bullets from expanding. If the BG's can't see you, they can't aim which reduces their probability of getting effective hits. Even if there is no cover available at all, one can still hit the ground and try to make oneself as difficult a target as possible. There's no point in being an easy target.
"And a moving man at short distances is very easy to hit. So, in many situations I'd still think: why waste time actually downgrading my chances?"
A moving man is not all that easy to hit, even at close range. A moving man is always going to be a harder target than a stationary man. While it is true that it downgrades your chances of getting a good hit on your first shot, it also downgrades your chances of being hit effectively, and IMHO that makes the movement worthwhile. IMHO if, and only if, you feel that you have the initiative and have gotten the drop on the guy should you just stand and shoot -- and you had better be right for your own safety's sake, and I'm not even going to get into the legal ramifications of that. You'd better be certain that you can shut down the threat before you receive return fire yourself, since you have committed yourself to be a stationary target.