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The fingerprint is your username, not the password.

You can tell everyone on the Internet your username if you like (most forums do), but that does not provide them access. The fingerprint is "this is who I am", and the password is "this is the secret to prove it". Anyone selling anything else DOES NOT UNDERSTAND biometrics. You cannot have a secret fingerprint any more than you can have a public password.

And fingerprints aren't unique*, because they aren't static, because they can be modified by simple actions, because they can actually be virtually identical from the start, and because of the reader sampling problem you describe, and thus can produce "flux" enough between two individuals that they are impossible to tell apart by fingerprint alone. Court cases rest not on "you are unique" but "you fit the pattern that only 1 in so-many people would have and you were also confirmed to be nearby".

[[ (*) Fingerprint uniqueness rests in the "every snowflake is different" area. Because there are a number of random variations, almost every fingerprint will differ from another. But because there are such a huge number of variations, uniqueness isn't guaranteed, merely suggested. And your own fingerprints are different on different fingers. It's this "pattern" that gives the random chance of someone leaving the same fingerprints - in the same order - at the crime scene billions-to-one odds. But there's no guarantee of uniqueness, and in terms of authentication they suck because you don't know if you're sampling the unique bits or not. ]]

The other problem is how easy it is to fake - there's no point them being "unique" if I can make a copy in ten seconds. The last fingerprint reader I used was a tiny 100dpi scanner with a rubberised surface. The surface was supposed to "splay out" your fingerprint, and the scanner merely scanned as any ordinary scanner does (they are mostly webcams etc. now). I got some Linux software and proved it by scanning in a document with it in 1 inch strips. Literally, printing the output of scanning my thumb and then putting it in front of the reader was enough to validate me forever after with a piece of paper. Similar tricks have been used on almost any amount of security measures since put in place in your average fingerprint reader. This is why banks, for example, DO NOT USE fingerprints on your credit cards, etc. They may be daft, but they're not stupid.

Something you have (fingers!), something you know. Otherwise it's not security, it's just convenience of not having to type in your username.