I found the core of the problem. The Tag Cloud module is broken. Everywhere every time. Whenever the code execution reaches Tag Cloud, everything is stopped. The front pages of the before mentioned shops were stock factory home pages with tag clouds early on the page. That's why they did not work.
When I visited another v3 shop the footer was missing and I saw the error message on the widget sidebar - the tag cloud was not working.
I have deleted tag clouds from everywhere for now, and every shop is working.
So here is it, you only have to check the TAG CLOUD code