IMHO, biometrics should be considered as "usernames".
They're not usernames, nor are they passwords. They have very different security properties from both, and don't fit into the username/password model.
The main difference from usernames is that usernames are not inherently bound to the person, but biometrics are. If I know your username, I can type it in and claim to be you. If I know your fingerprint, I cannot submit it to a proper fingerprint scanner (note that "proper" is carrying a lot of weight here). Said another way, in the context of a proper scanning and matching environment, biometrics do provide authentication. Very strong authentication.
This highlights, though, that all authentication value in biometrics comes from the integrity of the scanning process, which is why I said that it doesn't provide much when the scanning is done remotely, unobserved, with a scanning device under the control of the person allegedly being authenticated.
While biometrics fail as authenticators in uncontrolled environments, they fail as identifiers in nearly all contexts. The main requirement of an identifier, like a username, is that it be unique. Biometrics aren't.
Well, probably they are in some absolute sense, except for identical twins in some cases, but in practice all biometric matching is fuzzy because measuring bodies and matching them against templates is less precise than matching the bits of a username. Biometric matching is always testing whether the the livescan is close enough to the stored template under some complex distance metric. This means that given a large enough database you will get false positives. And thanks to the Birthday Paradox, this happens with a much smaller database than you might think.
To illustrate with some very rough and approximate numbers. Suppose that a biometric matching scheme has a 100,000:1 false accept rate (FAR). Suppose that this rate is absolutely consistent across individuals (pipe dream, but reality is way too complicated). So, you can think of it as a scheme that creates 100,000 pigeonholes and slots every individual into one of them. The probability of you falling into the same pigeonhole as me is 1 in 100,000. That's actually a very, very good FAR, BTW. I don't know of any commercially-available fingerprint or face systems that good.
Now, suppose I put a bunch of people in the database, and then you present your biometric and we try to identify you from the database. How many people can we put in the database and still have reasonable odds of uniquely identifying you? If we have 250 people in the database, odds are >50% that we'll hit at least one false positive. We'll match you, but also one or more others. What FAR would we need to guarantee a low probability, say 1/1000, with a database of a 1000 people? 500,000,000:1, or thereabouts. Nothing is that good.
The reason that biometrics are useful for identification in, for example, criminal trials, is that you don't (or shouldn't, anyway, it's happened, c.f. Prosecutor's Fallacy) convict a person based only on biometric evidence. You also need to have some other reason to believe they were in the vicinity, or had some motive, or something. They work extremely well as proof that an already-identified suspect was the perpetrator, though.
One other way in which biometrics are not like usernames, BTW, is that biometric scan templates are not really standardized. There are some standards, but they apply only to a subset of scanner types. In general, it is not possible to scan your fingerprint on your phone and send that to an off-device relying party for identification. It could work with face or iris imagery. Sort of. Face identification is much less precise than fingerprint. Iris could be good, I think. Also retina, except retinas change over time. Good identifiers should also be constant.
So, no, biometrics are not good identifiers. They are very strong authenticators, but only in the right contexts.