Moving magnet & moving coil are two different engineering techniques and don't necessarily refer to the output. Motor assemblies have coils and magnets and to create an electrical output one must move in relation to the other. In a moving coil, the magnet stays still. In a moving magnet - guess what? - the magnet moves!
If a moving coil has a large number of turns of wire, the output will be higher and then may not need the extra amplification that an MC stage will give, so it suits an MM stage.