Why should the Queen endorse the unions’ decision to choose a new Labour PM mid-term?

Imagine that the prime minister of the day — whoever he might be — were to stand down as PM and leader of the majority party in Parliament. His party would choose a new leader. The new leader would presumably become prime minister. I say ‘presumably’ because, according to my understanding of our unwritten constitution, it would be for the monarch to decide that this new leader was the person best placed to command a working majority in the House of Commons and, having so decided, invite him to form a government. The monarch’s task (runs the argument) would simply be to rubber-stamp.

Or would it? I’ll hold to that ‘presumably’ while I put to you a hypothetical question — a silly enough hypothetical question, I grant, but designed to test a principle. Suppose a party was returned to government at a general election, led by a man who promised to serve for the full term of that new government.