What do you think about doing it sort of like how RSA does their 2fa bits?

Say it worked like this:

You typed in your username, scanned your fingerprint for the rest of the username, and then typed a password / passcode?

That makes it virtually impossible to have username collisions (good) and still uses a password. If you were ultra paranoid, you could use a key fob such as a Yubikey and enter a OTP in addition to the above.

That would work, iff there was not a way to show that a particular person owned a particular username. However, I cannot think of any way to prevent that.

...But given the ease of getting someone's fingerprint I'm not sure if this is actually much better than a standard username+password combination (potentially with 2fa) without a fingerprint at this point, and it's less convenient to boot.

Tell that to Valve. I wish I could change my Steam user name that I chose in my juvenile years.

You won't be able to carry over games purchased, true. But you can create a new account.

You can't even do that much with fingerprints.

I have a main account and a little finger account.

Yep, you can do that 8 more times, total.

And you can't reuse a fingerprint if an account that you use a fingerprint as the user account for has been compromised.