I would be hesitant to draw too much from lab testing where the "target" knows what's coming vs how things really happen. Being able to side step while knowing its coming, under no other mental load (no verbal component, a very compressed and unrealistic scanning for pre-attack indicator, no weapon of your own, no goal other than to move, etc.) likely being compressed to move already, etc. in the instant an experienced shooter transitions to front sight focus is not particularly relevant to the real world. Watch videos of shootings and debrief survivors and you won't see much in the way of twisting or lateral movement, although lateral movement is (as you said) a big help in not getting shot. People who were stationary when the draw started are still stationary until the shot breaks, sometimes after. What you normally see is people rooted or all out running (either fleeing or for cover). Particularly for the citizen who's been able to disguise the draw or otherwise wait for diverted attention, I've yet to see attempt to dodge a shot by the bad guy. There's just insufficient reaction time to do so outside of lab conditions, particularly when under the mental load of being in the real event. The number of bad guys who've programmed a lateral step to the subconscious level probably isn't zero...but it's real close.
Raw speed hits diminishing returns pretty quickly. If you use proper tactics yourself, the window is longer than most think. If you use lousy tactics, you'll never be fast enough and will simply rely on luck.