The first scheduled the exit interview 5 months after leaving my job. Clearly said that they wanted to make sure I was comfortable in my new job before asking for feedback. I think the gap of a few months is a good mechanism to get honest feedback if someone is willing to provide it (and is what I now do for exit interviews myself)
Second time was with a manager I really trusted (I was leaving for other reasons). Gave him a list of the 15 things that I thought needed changing. When I visited almost a year later he showed me the list still on his office wall, with 12/15 items crossed off.
I think game theory might optimize for your own immediate gain, but overall many managers and companies want to do good, and your feedback might actually help if delivered the right way.