But a cracker can't "notice" that your password was a hash of "something" without knowing exactly what that "something" was, because the output of the hash is pseudorandom and isn't distinguishable from a random string.

Sure, they could assume every random-looking cracked password is a hash and try to crack each one, and conceivably discover your master password that way, but depending on your master password's entropy, that can be as unlikely as you need it to be. And the whole point of something like this is that you can use all your memory remembering an extremely high-entropy master password, rather than a large number of medium-entropy single-use passwords.