Or are hosting non-public services and want TLS certs that all my devices trust automatically, like me.

That's certainly an issue. There have been a number of cases where companies have demanded that people hand over domain that they "where not using". Not using being defined as "does not have a website".

It feels like there should be some way of determining if a domain is actively being used, to combat squatters, but when ever someone tried to make a rule it ends up being something stupid, like not having a website.

Email is one of the easier services to detect; not only does SMTP specify that the server sends a greeting before authentication occurs, but there's also a bunch of DNS records just sitting there in full view. I'd say it's easier to detect real usage with email than with HTTP, because, to my knowledge, nobody runs an MTA just to say 'this domain is for sale' like they do on the Web!

Including me.