The ability to serve a file “www.example.com” in no way demonstrates ownership of “example.com”; it demonstrates that you control www.example.com.
If you want to prove ownership of a second level domain you must do it through a record in DNS, or through demonstrating control of something that is publicly known to control the domain such as the administrative contact emails.
This really is a solved problem in the PKI space; they should have borrowed that rather than invent their own.
Unless the UI makes it clear it was verified with "non-primary" methods so users can be cautious, any method of verification is essentially "primary" from the user POV.