But there is absolutely no evidence at all that the system here is any better than the one in France, Germany, or the United States.
There's plenty. First off, the entire civil service and army swears allegiance to the Queen, not to the Prime Minister. This is very important, because the Queen doesn't actually control them, and yet it also takes an element of power out of the hands of a single person, the Prime Minister. It means if a Prime Minister engages in shady business, civil servants are committed to serving the Queen, not him, and theoretically could expose him as their allegiance isn't to him.
The Prime Minister cannot act like a President, and derives his authority from the Queen. The Queen is the head of state and symbol of unity, not the PM, and this prevents the PM from holding too much power, and prevents too much power from flowing to his head, as he is simply not supposed to be the head of state, or act as one, but as a minister and one who manages the kingdom.
As an example, when the Iraq War happened, Tony Blair got a boat-load of criticism for what he did. George Bush also got criticism, but there's more hesitation in criticising a standing President, who embodies the state executive, rather than criticising a minister of the Queen for mismanaging her country.
All in all it effectively restrains the elected leader from having too much power, by investing it into the monarchy, and power which the monarch can't even use.