I gave Kizaru's vivre card some thought and noticed that we've probably misinterpreted it:
On both available translations(Artur's and the initial one from Arlongpark or WG[?])they mention only proficient Haki users can "grasp his movements" or "capable of spotting" him.
Obviously, as we've already know, being capable of seeing the future alone doesn't simply make you faster. BUT - the way it seems to be worded in Kizaru's vivre card makes me think that CoO genuinely improves one's ability to perceive speed and as a result improves/allows one to improve their physical reactions. This makes sense because there's probably a very limited number of people capable of reaching a level where they could tango with Kizaru, and they're the very(very
)strongest.
Also, something interesting I noticed:
Note the way he charges his beam -- it looks like he's absorbing light from his surroundings. And I just noticed how most of the laser beams in the series behave the same way.