We have natural experiments of this: retirees, both early and otherwise. Do retirees during the first five years of their retirement "find productive work voluntarily" (your choice of words, not mine) in quantities that are comparable to what they did at work during the five years prior to their retirement? Not exceptional individuals, but on average.
I retired circa five years ago and spend my time doing stuff like walking the dog, drinking coffee and reading books, much like other retirees. My productivity is as close to zero as I can muster, and it is the rule, not the exception.