Even if the insights were less likely to materialise after stepping away, there would be plenty of cases of this happening, so the fact that virtually every mathematician can remember few of them wouldn't be surprising.

Point taken. I guess the likelihood ratio for this strategy being actively helpful is closer to 1 than I had previously thought.

However, it's not just a few incidences. It's remarkably frequent. And it's also still valuable to note that problem-solving can occur in the background without the need for conscious attention. Even if the background process turns out not to be as efficient as conscious reflection, freeing up attention while still working on the problem looks like an obvious win to me.