I'm waiting for the day in which I can sign up for 2FA without giving my phone number. At this point, I believe they are holding it on purpose, as my phone number is a much more reliable unique identifier than my username and/or cookies.
(Yes, you can use the Google authenticator, but no, you can't do it if you haven't given your phone number first)
Edit: by "they" I mean GMail - other sites work just fine.