Back in the olden days, or in other words, when I worked in the Civil Service in the early 70s, one of my jobs (as a lowly minion) was to answer any letters addressed to the Queen that vaguely came under the remit of the Department of Education and Science and pertained to the North West of England.
In those days, even the weirdest letters, even those that began Dear Queen and were written in purple crayon with multiple underlinings in red, got a polite if non-committal reply. Not generally from the Palace, it's true. The correspondence was normally passed to the most appropriate government department. (Which is where I came in.)
But those who, like papersky who wrote sensible letters, got sensible replies. *g*
I do hope they still do. I would hate to think that standards had fallen so far that correspondence was ignored.