If your password is never stored in plaintext, it's less likely to be leaked, either maliciously or inadvertently. It's the same rational for not storing plaintext passwords on a Unix system.
Like on a Unix login, I have to provide the actual password to the service. But measures can be taken to ensure not only is the password itself never stored, but even that the memory that contains the password is appropriately zeroed after use. It's not a matter of the user trusting the service, it's a matter of the service being cautious with itself.
There's no need for a new protocol; lots of websites manage to never store passwords today. I guess your protocol does provide some assurance that the other end isn't going to store anything but the hash. Unfortunately, anyone competent enough to implement it is already probably doing the right thing, and the people doing the wrong thing frequently have business reasons for doing it wrong.
Like on a Unix login, I have to provide the actual password to the service. But measures can be taken to ensure not only is the password itself never stored, but even that the memory that contains the password is appropriately zeroed after use. It's not a matter of the user trusting the service, it's a matter of the service being cautious with itself.