> This is true, but it sure would be helpful if they could give qualitative feedback like "the impression was that you were strong in a and b, but weak in x and y." That doesn't seem like too much to ask

Sadly, even this kind of feedback exposes the company on a legal front. There is a lot of precedent coming from rejected candidates who ended up suing the company because of this kind of feedback.

The only sane thing that a company can do from a legal standpoint is say "Sorry, we don't have a position for you at the moment, good luck in your search".