When I was in uni, I found that just having a boring cover letter drastically increased the odds of an interview (for internships and post grad work). I bet a lot of places just have a filter that adds you as a higher priority purely on the existence of a cover letter.
I've never read a cover letter that I found valuable for hiring anyone, though. And I'm sure mine were never of any actual value either.
I like that insight and should I ever be back in the kafkaesque nightmare of blind online job applications, I will take your advice. As you point out, barring typographical mistakes a cover letter being too generic isn’t likely to result in a rejection, but not “checking the box” very well might.
May you never have to write one again, but if you do, it might be helpful to think of the cover letter as a reflective writing exercise. You might be able to gauge your level of interest in a particular role by how easy it is to write about, for example. Or it could just be some practice at communicating your strengths and abilities (this would definitely apply to me).
IMO it's too disheartening to put effort into such personal writing without the awareness of some kind of direct value or benefit, since chances are it's going straight into the void.
I've never read a cover letter that I found valuable for hiring anyone, though. And I'm sure mine were never of any actual value either.