Thanks for answer everyone!
There were couple of useful advices/suggestions. Like one with trying case 6 (I used case 4 until now), and that maybe delay in firing after half press is possibly responsible, and suggestion to go for really high shutter speed, use M mode and auto-ISO, also comments on the closer focusing distance are spot on, most of the problems are at the close focusing distance. Comments on 50 1.4 being hit and miss also accurate, seems to be one of the worst offenders I have, though I can make any lens miss, easy...
Most of other things I tried and knew. Summary of answers:
- I don't think camera is a lemon, it must be the owner

, as I had the same situation with 5d mkii
- I never let camera choose focus points. I mostly use one point, central point most of the time. I use servo when kids are on the move, or if I don't need to recompose at all. MY DOF button is configured to switch mode while being pressed, so I liberally move btw. one shot and servo. Obviously, I'm not quite a beginner, and still so many misses.
- I aim to place my chosen point on the eyeball, absolutely ALWAYS.
- I did AFMA some of my lenses, though it's possible I didn't do it well
- I'll take exception with analysis that elbow is sharp on the first picture. When I look at 100%, I don't see real focus anywhere. No clean fiber. Not that 100% matters, I was just trying to figure out what happened.
- I do get quite a few keepers, and my percentage of good shots is maybe 50% for (rental) 24-70L II to 20-30% for 50 1.4. Maybe that's to be expected? But where I'm getting annoyed is that many times kids do stop for a second and still many of those pictures are to me inexplicably smudged.
Look, couple more examples, any theories are welcome:
1 - just slightly annoyingly unsharp.
2 - There is nothing truly in focus. Yeah, it looks like sweather is in focus, but not true. Check third picture to see how sharp it looks like. Much better, right, so it makes me think it's not only OOF issue, but camera shake?
3 - this one is sharp
Perhaps I should have chosen something more obvious, but this is 24-70 II, pinnacle of lenses right now, and it does seem better, i.e. keeper percentage is higher, and unsharp pictures are less unsharp. (English is my second langauge, so please no jokes
