It's more about "accepting and publishing arbitrary content".
But, in practice, how hard is it to host a website anonymously? Or off-shore?
Obviously it is trivial, but so is shoplifting.
Both are illegal and telling people to commit crimes is not helpful.
In Germany it is straight up illegal. The UK law has provisions where a services has to name a responsible person or report specific things to the government. Obviously those can not be accomplished anonymously. In any case hosting a website anonymously doesn't work if you want to work within the law, any lawsuit against you will identify you.
> I don't even have to provide my personal info to register a domain name, I can run it on an IP-address
Which is totally irrelevant. I can also go into a store and take something without paying. The question is whether that is legal or not and what you need to do to keep it legal.