Passwords are broken for precisely this reason. You are operating under the fiction that permanently handing over entropy from a limited source to an untrusted

Passwords are broken for precisely this reason. You are operating under the fiction that permanently handing over entropy from a limited source to an untrusted party, even through a (for a time) one-way function, is ever a good idea. Please do make all password hashes public. It will finally force the move away from passwords.