I'm not sure I even agree with the premise. Politics and "discourse" around it, especially by common people, has always been crass. It's just that those common people have a megaphone now that the internet exists.

a) It was created by a comedian, and it's an amusing name

b) It's easy to remember

c) Many people are legitimately angry about this kind of thing and using profane language (such as it were) seems warranted

I don't disagree with your feeling about this, but just to clarify:

The domain gofccyourself.com was set up by John Oliver's show, "Last Week Tonight," and their modus is to use humor to draw attention to tedious but important issues.

Politics is mostly entertainment. Either comedy or rage porn.

To get attention. Politics is not an exception, its used everywhere.

Same reason that politics is often violent.

The edginess got your attention, did it?