I shouldn't have to explain this, but a letter is a medium of communication, that could just as easily be written by a LLM (and transcribed by a human onto paper).

Communicate between what though?

Communication happen between two parties. I wouldn't consider LLM an party considering it's just an autosuggestion on steroids at the end of day (lets face it)

Also if you need communication like this, just share the prompt anyway to that other person in the letter, people much rather might value that.

I shouldn't have to explain this, but a letter is a medium of communication between people.

Automated systems sending people unsolicited, unwanted emails is more commonly known as spam.

Especially when the spam comes with a notice that it is from an automated system and replies will be automated as well.