I answered a question (Should I use capital or small letter here? "Dear All" or "Dear all"?) about capitalizing "all" in "Dear All," In answering this, my thinking was "what function does "all" serve?" Today, while answering another post, I came across a website discussing the use of a colon (http://www.grammarbook.com/punctuation/colons.asp). It states that in formal greetings you should use a colon after Dear Mr. Jobs, as in "Dear Mr Jobs:" In my writing classes, I teach students to use a comma after the name and after "sincerely," (closed style). When I was growing up, I remember seeing the colon used a lot, as well as "Sirs:" These usages seem to have gone out of fashion. I know that open style does not use comma.
If, as the writer of the wesbite says, you should use a colon, X has one function; if you use a comma, another function; and if there is no comma, something else. Also, we call "Dear X" a salutation but it is the beginning of a sentence. Did people in English at one time start letters with more full "openings" such as "My dear Constance, ..." so the comma makes more sense? What about in ancient times? Did the Romans use a comma or no comma after "Dear Cicero[ ] I hope this letter finds you well in exile."
So, in a letter, what function does the "X" serve in "Dear X" and what function is the phrase "Dear X?"