I'm not sure this follows. You're allowed to publish, say, a book or pamphlet without signing it with your legal name and address. So is a website more like a book, or a building?
Somewhere in the middle IMO. If the domain name is desirable it looks more like a building, because people generally care about who owns the land when it is not getting put to good use.
Websites are more like books when they have a domain no else else cares about.
So, maybe require official ID/address/contact info for any domain over a certain price? Or for all domains under a certain character count, maybe, which could vary for TLD.
How do you determine the value of a domain name? Also there's nothing particularly valuable for most short domain name strings except on .com. It's generic words that tend to be valuable, not a short random string.
Websites are more like books when they have a domain no else else cares about.