That's how my dentist's billing website works. Except it's limited to 8 alphanumeric characters, not 10, and they were quite happy to accept my pasting a 16-character generated password into the field. Unfortunately, they don't have a password reset link; instead, the you call the receptionist and they read out your password to you over the phone. This isn't a legacy system, either. I can only imagine the backend is written in QBasic or something.