What if you use a cheaper hash function (e.g. bcrypt with a lower work factor) on the server? The bcrypt hash is the password, but a very long one compared to t

What if you use a cheaper hash function (e.g. bcrypt with a lower work factor) on the server? The bcrypt hash is the password, but a very long one compared to the password that the user entered, so presumably it is very expensive to brute force even with a relatively cheap hash function.