First of all, thank you very much for at least trying to get me some help!
Yes, if you wan't to customize the path of the PHP-FPM unix socket file, then you may be out of luck. (seems to be hardcoded somewhere)
This is what I had first thought, because I can't find any relevant string anywhere by just grep-ing the template folder. I don't know if there are better ways to search, if that's the case, I'm willing to learn. But hope someone proves you (and me) wrong.
But as you want to use the very same socket config/file for all sites, it would also not make sense to let every domain create this file. (will most likely throw errors anyway)
Don't get me wrong, let me make things more clear. I had first asked how to use the same TCP endpoint for every site and get a relevant config file for the php-fpm service (i.e. set the conf file to listen on TCP port 9000), but then, also based on some of the downsides you had pointed out which are indeed something to worry about, I switched to asking how to get a different config file for each domain, which is the default and works flawlessly, but placed in a path that's different from the default, outside of the pool directory.
So you just create a /opt/plesk/php/[phpver]/etc/php-fpm.d/MYCUSTOMCONF.conf file manually and adjust the pool name and the path to the unix socket file to your liking. (or change it to TCP socket)
I have already tried going this route, it does seem to spit out random errors, but maybe that's just me and my config.
To sum it up, I'm still left with trying to change the default socket path to something different from /var/www/vhosts/system/$pool, and define it in the prefix directive in /opt/plesk/php/[phpver]/etc/php-fpm.d/[domainname].conf