I agree with you, except that the company should send out a rejection letter as soon as they can. If I were hiring, I would only send a non-generic response if the rejected candidate specifically asked me if I would be willing to give her or him constructive feedback, or otherwise indicate why they did not get the position.
What if they are not rejecting you? What if they like you as a candidate but decided to move forward with someone else (and it was a tough decision), and want to wait to see if that person will work out. It sucks, but it happens.