At my company we actually have the feedback written up, we just don't share it with the applicant. The reason is that some people just can't handle getting negative criticism, and if you give it to them will not believe it and instead think that it must be discrimination. Then they start harassing the company or try to file a lawsuit. This is why a lot of companies have a policy not to share feedback with the employee, because it protects them.
Even if it is only 1 in 100 applicants who is like this, they can cause enough trouble to scare employers off of sharing feedback. Especially because there is no particular incentive for employers to share the info.
Then why write any feedback? That doesn't make any sense.