Have you ever been on public transit in DC? There are billboards all over the place (or were a decade ago when I was there last) that are clearly sales efforts targeting like 4 people. It's not that weird.
If you write a letter to the newspaper, you might hope to influence one person, or the general audience of the paper. If you feel so strongly about something that you compose an op-ed, you'll also have to do the work of persuading a feature editor to publish it (although this isn't too hard, if it seems like it fills the news hole). That's a bit less accessible than a letter to the editor. If you're buying full page ads, you're leveraging capital that most people don't have to go outside of regular interpersonal communication channels.
I've priced doing billboards just for funsies --- to make a (snarky) point, not to make money. It's not that expensive! Also: how could it be? Look at some of the terrible billboards out there. There are a series of I-55 billboards advertising a single self-published book of poetry.
Your original statement was "normal humans don't try to communicate directly with each other through the media". I think you're using a pretty idiosyncratic definition of "normal" there. The phenomenon you're labeling abnormal is I think actually pretty common.