Guess what the send you when you forget your 2FA or password? Yep, an SMS. So out the door goes the whole point of 2FA. Your three factors (account name / email address + password + Google Authenticator) have now been reduced to one factor: your email address.
I can rent a mobile tower in Malaysia or some other asian country, advertise your phonenumber as roaming there for about €10/h and start intercepting all your shit. Or just get your telco's inept service dept to forward your number somewhere else.
Lessons here:
1. Even the giants get it wrong. 2. There is no security anywhere in the tech world. Literally everything is broken. Your electronic car locks / starter system, your phone, your internet, everything is horribly horribly horribly broken beyond any imagining, even for hyper-tech savvy people. 3. Remove your phonenumber as a backup device from your google account and never use it as a backup device every again.