[wavelen]

afair you need to set up a phone number before you can choose to add another 2FA option (which is stupid imho)

[UncleMeat]

Even if this is the case, this isn't a problem for the poster. They have a phone number, it just changes frequently. They can sign up, enroll in a TOTP or U2F system, and then they are set.

[yellowapple]

Except if you're using e.g. Google Authenticator and you lose that phone, you've now lost your TOTPs. The most unhoused-friendly solution there would be to use something like Authy instead (which is another password to remember, but at least it makes it easy to recover your TOTP keys on a new device without needing the old one); next best would be to use something like andOTP which supports backups (but then you'd need someplace to store those backups, which introduces the same problems as safely keeping a phone on your person).

[borissk]

It's not stupid - Google wants to track everyone everywhere and a phone number is a good way to link an account to a real world person.