You can disable SMS on Fastmail after you enable 2FA. I had asked their support, and IIRC the trick is to hold down CTRL when you're on the settings page, which will enable the "Disable SMS" option.
You wouldn't be surprised if you saw the amount of people that said "hey can you remove my 2FA? I kept my codes on my phone and it broke".
It's a real UX issue, the average person just can't back up their TOTP codes at all. Hell, I have a Yubikey as a backup and enroll the TOTP code to both places, and to the Yubikey as U2F.
This was years ago, so YMMV.