I gone through a lot of hosting service providers and unfortunetly cannot find a single one that can be used without running nonfree programs, all of them require loading bulky obfuscated JavaScript apps.
I know of Codeberg Pages for static sites for example, but it is not suitable for any business or professional use.
But as I said: once the DNS entries are set up, everything is routed directly to your machine. What runs there is completely in your hands. Same with VPS/root server: SSH is free. Pick the client you like.
I don’t know of a single registrar or hoster that I can’t run without libre software.
I get thy stand on this, personally I also have to compromise my software freedom to register my domains, but again OP asked to avoid X and saying after doing X you won’t have to is not answering the question.
But he said “proprietary software to run”, not to “setup” or “register” or whatever.
Ah yes, I bet thou canst also skip the booting part when thou runst software on thy compooter. And Jehovah (or an idol of thy choice) forbids any configuration or upgrade requiring a reboot.
If thou dissectst this even more clearly thou wouldof noticed OP asked about running a domain registrar or hosting provider, not using their service. Also the word was propietary.
Now, if thou excuse OP’s imperfect English thou can find a clearer description below:
Like virginity, it’s either with or without innit, or doth thou prefer thy olive oil lightly fucked?