That's all fine and good but reliability of delivery of 2FA data is not exactly fantastic (especially SMS, which lots of people use for 2FA), besides that it gives google your phone number, which not everybody may want to do.
So don't use SMS.
TOTP authenticators don't require any data to be transmitted at the time of authentication. They're set up with an initial shared secret (typically transmitted via QR code) at which point the codes are generated independently on the two devices.
This means the TOTP device doesn't even need to be connected to the internet. As long as you can get the TOTP seed onto the device (worst case: type it in), you can use that device for 2FA.
I could set up TOTP on my personal account today, again without linking it to a phone number, but I don't because TOTP is less safe than my Security Keys which are already enrolled.