Musket, you either don't know or are ignoring a significant
difference in roles between the Queen (and the President, in the US) and the PM.

There is an interesting anecdote from WWII times, that tells
of a ceremonial international banquet attended by Churchill and
Roosevelt.

It seems that Churchill complained (perhaps with tongue in
cheek) to Roosevelt that the protocol officer(s), in planning
the occasion, had seated Churchill in a less-preferred seat
than Roosevelt's at the table.

The story is that Roosevelt replied something like, "That's because
I'm the Head of State as well as Head of Government, whereas your King is the head of State and you are only the Head of Government."

Apocryphal? I don't know, but it does somewhat illustrate the two
roles.

Dave Oesterreich