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Any domain registrar/hosting provider that does not require propietary software to run?
(discuss.tchncs.de)
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You can use Ansible to create domain names and register URLs on most popular hosting providers/registrars.
You shouldn't avoid platforms just because they have non-free websites, that's extreme bro.
Yeah. The idea of not using a domain registrar because they optimize for the 90% use case (web management) seems pretty extreme to me. But if OP is against web sites, I don't know how they'll read the docs for something like using Terraform to manage domains at Cloudflare. It is an option but it's also the 10% use case.
Heck, if you want to really want to be a luddite you could use the raw API! :) Most hosting platforms/registrars can be commanded with just curl.