I mean don't get me wrong, the stories don't tend to be anything crazy, and they're basically never the center of the game. Like, you're not going to find a story on par with The Witcher 3 in an idle game. They're usually just there to give a justification as to why you're doing things, and in some games it's pretty obvious that the gameplay was designed first and the story was more of an afterthought.

I don't mind that personally, I've never been one to seek out games just for their story.

If you are interested in seeing how a clicker game can drive a story I'd recommend taking a look at https://www.decisionproblem.com/paperclips/index2.html only takes an hour or so to play to completion iirc but its pretty interesting.