In most cases there's no answer beyond someone else seemed like a better fit for the position. How would it help to know you would have got the job if only this other person didn't apply?
1. It gives them a kind of closure and treats them with respect.
2. It can help them improve for future applications.
Usually, the reason is not "Someone else is a better fit". We're not just trying to fill one position -- if we find good engineers, we'll hire them. Usually feedback is related to stuff that came up in either the coding project or the interview. It helps people in the same way that code review helps them: by giving them an opportunity to learn and improve.
This is an excellent basis for a lawsuit.
(edit: I wonder if we're talking about slightly different things here. The "notes" I'm referring to are primarily code commentary -- the same kind of material we cover in pair programming. As far as I know, we don't share notes about our internal decision-making process, which perhaps is what you're talking about.)
great way to look at what bothers us all after a rejection - thanks