A combination of "something you know" and "something you have" is always going to be a very strong authentication scenario, and making "something you have" a non-hackable thing that truly only you can have (i.e not a USB key or a TOTP seed etc.) is a good choice.

The catch here is that when you mention biometrics, you make the assumption of static biometrics (rightfully so, as most methods like Touch ID and Face ID are static), but if you combine lets say face biometrics with liveness checks, you are getting into a territory where faking them becomes much much more difficult (there are various mechanisms out there, the good ones rely on completely random interactions and light-bouncing detection methods as an example).

The real challenge is how do you make these very strong biometric methods frictionless and cheap? Or how do you introduce similar controls - like liveness - for easier methods like fingerprints?

And using any of these (ideally) has absolutely nothing to do with anonymity. You are not anonymous online regardless of what you use for authentication - and you are frankly not smart if you assume thats the case. A company offering a service with biometrics is no different from a company doing the same based on email/username and a password, if they do privacy and security right.

I could actually get into a much longer rant about this last part, as it blows my mind how many netizens are all about privacy and whatnot, yet are willing to expose every single detail about them when its convenient from them...