The idea is not to move yourself out if the line of fire, the idea is to survive!! Too many individuals buy into the move to cover, draw weapon and defend self/family from cover or try to completely leave the area. Gunfights/ violent attacks are fast, dirty and scary. Logically, you can not out run a bullet. Google fatal shootings and you'll have access to thousands of articles detailing Gunfights/attacks. Where do these attacks occur? I'll help; driveway/front yard, gas station, apartment/ house, basketball court, night club and street.
Now, how many of these places offer adequate cover ( not concealment)? If you can name any, how fast can you run to these positions of cover if you were attack or in near proximity of a gunman? You would mostly be moving on a linear path, do you think I could walk rounds onto you while you were moving to cover? If no cover was available could I put rounds through your concealment?
In most situations you are more likely to survive if you immediately engage and end the threat. This may be from a traditional or non-traditional shooting position. Hit statistics in shootings is historically low, moving and shooting under stress is not recommended.
Lastly, "combat" is mostly static when it comes to shooting. If engage while on the move, you will be moving forward slowly. Think slow is smooth, smooth is fast.