I'd prefer something such as Microsoft's Passport/FIDO 2.0, which authenticates users with online services based on their local authentication with the device.

https://www.youtube.com/watch?v=amBknB1nOYE

With Google being a member of FIDO, I assume they will adopt it when FIDO 2.0 is ready anyway, but it's good to let them know ahead of time that we want it.