This sounds like something your ID card would be suited for, German ones already support NFC and can used to authenticate against government websites.
Of course that would eliminate anonymity, which would be horrible, but maybe ok for Gmail where people use their real names anyway.
But in the event of loss of ID card or identity theft, there is a trusted instance (the government) that can block old ones and issue new ones. This could be used as a reliable way to rotate a 2FA key, because some unique number attached to a citizen won’t change.
The worry is that if systems like this become widespread enough then they'll simply be required just like phone numbers are. The website will pinky promise you that they won't sell your data. Not to mention that now the government can just request access to all of your accounts on all of these services, because they know you had to use your ID.
Of course that would eliminate anonymity, which would be horrible, but maybe ok for Gmail where people use their real names anyway.
But in the event of loss of ID card or identity theft, there is a trusted instance (the government) that can block old ones and issue new ones. This could be used as a reliable way to rotate a 2FA key, because some unique number attached to a citizen won’t change.