This is a great idea! One feedback is to integrate so that people can SSO into their registrar, not sure what it would take to do that but I was setting up something through Google and it automatically detected my cloudflare and was able to let me sso to change it instantly.
Also some kind of list or search page that showed some domains (even if you didnt search yet) would be cool and maybe encourage people to use it.
Also, it would be nice to be able to save the domain even if it's not able to verify (since I just added the TXT record)