While I agree that feedback would be nice, I also think that if you objectively evaluate the application/interview engagement, you can narrow down the reasons for rejection. And after a few interviews you can start seeing what the patterns are and make adjustments accordingly. I think it is much more informative to try and get honest feedback on your resume, application process, and interviewing skills from friends and acquaintances. Pass your resume around to friends who work in HR and ask for feedback. Do a practice interview or two with someone who works in a similar job to what you are applying for.
It's also worth keeping in mind that the process for many companies is very random. At my old company, I have recommended a few very qualified candidates, only for their application to get stuck in HR limbo due to budgets or politics. And on the other side of that, every now and then we would open the floodgates, and any one with a pulse would get in. It was really frustrating, but that's just how it works.