If we mount something on the back of display, it can be not only Mini-ITX, but also mATX.
Anyone knows good suitable or modded cases for this setup?

Coolermaster makes the Elite 100, which will take MiniITX or MicroATX boards, though the latter may have some items blocked as they'll be under the PSU.

I have one and it works pretty well. I did a test mounting to a monitor, but I'm not using it that way at this time.