You don't have time to write custom cover letters everywhere. But sometimes, there are crazy people in departments (we have a couple) that read every single cover letter when on a search committee (I never did). It mainly comes back to signals of gettability, and geographic presence. Its a cost on you and a non trivial one to customize a cover letter. So if its a place you really love, I could imagine customizing your letter for a few places. But will it guarantee an interview? No. And not all departments will have people that bother to read through 800 cover letters (we received over 800 applications the last time we had an open search).
Funny story, when I was on the market, I accidentally sent the wrong cover letter to Cornerstone Research (they got the Bates White Cover Letter). When I was on I flyout there, they brought this up to and laughed about it. I think it didn't hurt me there, because it suggested I was applying to all of the litigation firms which for them was a positive signal because they want to separate out who's going to academia and who isn't.