In our case, it's not an iron-clad no feedback allowed policy. We're just much more careful about giving it, approval is given on a case-by-case basis.
A good typical whiteboard interview naturally includes hints, feedback, and collaboration. After several hours of it, we have a very good idea of how well they may respond to feedback from members of our organization.
Honestly, I love giving feedback. I love helping candidates be better at interviewing. Bad interviews are painful to the interviewer too. I'm out of a small market so people and word gets around.
If it really isn't their fault they didn't get the job, we try to make that very very clear. It really sucks when we have to pass up on someone who absolutely killed the interview because someone else did better.
The harsh reality is, many people that don't pass on the interview are people we do not want in the industry. The good ones we give every hint and help we can.
There's also more tactical ways of extracting feedback from companies rather than directly asking for it. We can't tell you about how you did well after rejection, but we can talk about what our expectations are during the interview; put two and two together. I've noticed the good candidates that are serious about improving their interviewing do it, and from the company side, it's a strong signal they're not trying to contest a decision.
Food for thought, when was the last time you gave a company feedback on their interview process? I've traded feedback for feedback quite successfully many times when I was interviewing.