Why does the random button even exist?

{quoted}

It has literally no purpose unless you're with your friends and decided you would all pick a random champ.

You just answered your own question.

For fun maybe?

I've Random selected champions with a group of strangers before. Everyone random picked.

Happened to be a legitimate comp.

What's the point of a random button in every game then? Unless you truly don't have anyone you don't want to play one bit and you don't care at all who you get, it's pointless, other than it's fun.