In terms of things like police and military and actual self-defense, speed is kind of a luxury. More important are things like steadiness, awareness, and, as they put it in some movie, 'How fast can you take your time?' When adrenalin kicks in, speed is not your problem. What to do, and do well, is.
Natural speed is a gift, and devotion to training it is, ...cool, but people trying to be 'fast' tend to not be putting the energy where it belongs, so it's not really something for training people in the real world. People trying to be 'fast,' they're generally telling you everything they're about to do while trying to build up for speed. Doesn't matter how quick they are with a weapon if you know where to place a stall or take a step or just plain be well on your way elsewhere.
People with weapons tend to think with them. As someone who used to actually be darn fast, that's usually how you get home that night.