The problem is that a certain fraction of applicants will become convinced, rightly or wrongly, that they were hard done by, and were blackballed for whatever reason. Any hard information you give them can be used against you.

And unfortunately not just obvious stuff like "we didn't hire you because you're black". You can say something innocuous like, "your grasp of algorithms didn't seem strong enough" and the candidate will flash to a particular interviewer who asked an algorithm question they didn't get, and become convinced that that was who blackballed them. And can further become convinced that that person actually had it out for them for unrelated reason X.

This might be unlikely to wind up in court, but it happens often enough that it shows up in nasty blogs, rumors, etc that every large company has learned that you just don't want to go there. And none of them do.

So instead you sue them based on the claim "they didn't like $RacistReason and wouldn't even give me a real one".

How is that supposed to help?

I think the danger with getting sued is even one single successful claim will cost the company in millions, not to mention the publicity.

Even an unsuccessful claim could cost tens or hundreds of thousands to defend.

Plus the fact that the upside (if any) to revealing the reason for no-fire is negligible.