And yeah the British monarch's theoretical legal power is immense. For one thing the UK armed forces swear loyalty personally to the monarch, not to the government! The monarch could go to war with Parliament again and the military would be upholding their oath!
The late Queen was a woman of impeccable public ethics though. In some sense it's more admirable for a person who is not bound by the law to choose to follow it scrupulously, which she did.
I think it's fair to say that Elizabeth was exceptional for how she handled her position as Queen but the United Kingdom is always just one "King" away from a disastrous ruler and that could get very ugly very fast and potentially for a very long time.
That said, same could happen here and for much the same reasons, which basically comes down to issues of common sense and fealty. If the first is low and the second high the odds of getting caught up in a shit storm are pretty good.