Not always a possibility. Many banks require phone number based 2FA, for example. And you're required to use it any time you want to make a transaction that exceeds some threshold.
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.
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).
The context for this post is a person who moves between countries frequently and therefore gets new phone numbers. This person has consistent access to the same phone.