This is the one argument left for monarchy; that the military in the UK (and technically Australia) swear loyatly to the monarch, not the Prime Minister. In the event of an obviously-lunatic elected official ordering the troops into civilian areas to "pacify" civilian populations, the monarch could (in theory) countermand that order.
Isn't that worse? You don't even get to elect the commander in chief, its just some random guy who was born into it?