If there's a short between phase and the earthed case, then it will protect the device, but you're right, a fuse is required to protect against fire from phase to phase or neutral overloads.
Also note that a fuse isn't there to protect the appliance, but the cable. There are few things which are capable of protecting semiconductors inside the device. Slow blow breakers/fuses can protect motors from over-current and thermal fuses/bimetal strips can protect against overheating and fire.