I have seen ham radios all over the Wasteland and have no clue about what they are for, in the game. I used to click on all of them "just in case" but have given up. I also saw them in New Vegas with pretty much the same results.

Do they serve a purpose, other than frustrating an OCD like myself?

Spoiler free ~

Lol, usually they serve no purpose but on occasion you will "pick up a radio signal" from one that you might want to follow.

hmmm.... Guess I'll keep clicking, but now watch "extra close" at the upper left hand of m,u HUD

Actually, it is not the Ham Radios that are the source of the signals you want to follow. It's other radios. Some you have to throw a power switch at a substation or power plant to activate, some you just stumble upon. So, leave your Pip Boy radio on, and you will get the other signals. (Maybe it just tells you the signal is present, can't remember)