You mix two different things, AF time and shutter lag (which is the time that elapses between pressing the shutter, with a focused image, and actual picture being recorded. Both are important, and there is also the shot-to-shot time, i.e., time taken after the shot before next picture can be taken. All this is, indeed very important.
Anyway, while it is true that the reviews don't mention all that in detail, I have just been looking at the Olympus mirrorless OM-D review and there is a discussion of the subject (under 11. Performance)
|Mig-17-1 by bbmach|
from Low Pass
|Rotting Gracefully by Mond|
from Natural Decay
|attic by wgjohnston|
from In the attic, or in the basement!
|Ox Bow Aspen by McFrost|
from cell phones - nature photographs