> All feedback is anonymous, rolled up with non-exit feedback, and delivered to managers/leads periodically so it can't be easily linked back

Oh sweet summer child.. No feedback is anonymous, ever. It can be 'confidential', which means that HR can disclose it at their discretion or as appropriate.

As a manager, if you get value from the exit interview, with all due respect, you're doing it wrong. All the feedback which could be part of the exit interview should never be a surprise or an added value after the fact.