The issue is that if an attacker can eavesdrop on a compromised authentication server, then it can record user's master-key and thus he will be able to impersonate user without issues until the password gets changed (i.e. the derived master-password is actually plays role of a password now). With PAKE this issue simply does not exist.
Via the master-key, the program derives(locally) the key to encrypted the data and a different secondary key for authentication against the server. without knowing the master-key you can't decrypt the vault even if you were able to trick the server into sending you the vault.