So, I did some testing to see if I could figure out under what situations it goes up to three seconds (to go to Playback).
And what I have found now is this: It all depends on what lens, the zoom setting AND focus setting. I don´t know in what world this makes any sense - not in mine.
So, using the 16-80mm, if I set it to 16mm and focus infinity, then it takes 1 second to go to playback (from pressing Play button). If at 16mm and close focus, I get only slightly more than 1 second. If I go to 80mm and infinity, the time to get playback is still about 1 second, but if I go 80mm and close (minimum) focus, it takes 3.5 seconds to go to playback. That is, three point five seconds!
With my 23mm f/2, the times are: Infinity: 1 second. Close focus: 1.5 second. Not alarming (but still a bit weird if you ask me.)
My Samyang 8mm fish gives you a taste of what the X-H2 is capable of. Press Play, and you will see an image 0.5 seconds later, no matter what. This is the kind of snappiness I was expecting from a "flagship" camera. And I really, really hope that Fuji can get their stuff together and fix this nonsense. I will definitely send them a letter.