Yes, if a system is storing your biometric data remotely, then it can't be changed and it's a username, not a password.
But modern biometrics don't work that way, at all. The biometrics is stored client-side (hopefully securely and considerable effort is made to realize that hope), and it is used to access a private key which signs a challenge.
The biometric can be revoked, the private key can be revoked, all of these things can be changed by the user.
So let's say someone busts my fingerprint out of the TouchID secure enclave. That's not great (nor is it easy!), but they don't have an ability to generate a private key with it which Apple will recognize: that requires my password.
So I can generate a fresh key, confirm it with my password, and now my copy of the biometric works and theirs doesn't.
Edit: "courts or police can compel your fingerprint but not your password" is a completely different argument, and the solution is a way to rapidly lock out biometric authentication so that the password is a hard requirement. It also doesn't apply in a number of jurisdictions.
As a practical matter, actors who are unwilling to reach for the rubber hose can't get a password, while a fingerprint just requires the willingness to manhandle someone without injuring them, and that much is basically universal.
https://en.wikipedia.org/wiki/Password
There is nothing secret about your biometrics. Especially not while you are in detention.
That would potentially upend decades of case law - the government can compel somebody to produce a physical key (which now includes fingerprints and other biometrics) but cannot compel production of a passcode/combination.
This article talks about a case in the 11th circuit in 2012 and another in the Pennsylvania Supreme Court, Commonwealth v. Davis. Apparently the only time you can compel someone to give their password (which biometrics serve the same purpose) is if the state already knows what's on there. It's called "foregone conclusion exception."
Yet if the government can show that it already knows of the existence and the suspect’s possession of the documents at issue—i.e., that these matters are a “foregone conclusion” and thus that the factual assertions implicit in the act of production add “little or nothing to the sum total of the Government’s information”—then “no Fifth Amendment right is touched because the ‘question is not of testimony but of surrender.’”
You can be forced to submit to fingerprinting, which could also be incriminating.
Here's some interesting copy on similar cases.
https://arstechnica.com/tech-policy/2020/06/indiana-supreme-...
And should your username ever also be your password?