faster has many definitions, like acceleration time, end speed, reflex start time and so on.. gun fights are prob different tho I don't really know,, the part up to the trigger snap is only part one can time/ be there first so on. but with launched pushes, punches, stabs etc. usually started from a bit out of range or you would already be there, striking or controlling by then, faster is not the word I would use.. most people move, some move a lot and may look hard to control/strike due to speed, evasiveness etc. way I read it is few people move close to efficiently. I have teachers who move quite slowly physicaly, yet it is enough. As I launch, and cover the bit of ground to reach them, they are reading what I do. Most attacks, at my level, are more of an A to B, or pre thought out/planned target. The teachers efficient read of angles, timing, distance, force etc allow them to barely budge, but still be gone from your attack, and easily ( slowly physicaly) in on the attacker. Because they are aware, and move extremely efficiently, they can do a flowing move, that can adapt more easily to the needed adjustments as vectors change.
it can be either very frustrating, or very motivating, depending on how you look at it. I fought a lot of full contact successfully when young and was known for my quickness then. I am not a slouch now, and can still blur moves, but cant touch a teacher who seemingly is bored.
watching Muhammed Ali in his heyday when he would turn a jaw, sink an inch as he folded, and lean a touch, while 3 punches ripped by is essentialy the same thing.. efficient movement, based on timing, angles, distance etc etc. and lots of experience. Best performed in a relaxed manner..
All of us can do the same, tho not to that degree. Work with a partner who is stiff, telegraphs, tries to use strength etc. and move less, move slower, move correctly.
Speed is wonderful to have, relaxed moves are quicker, but they are one factor of 10 or more. So not the most important, unless all else is equal. Which it NEVER is