FWIW, my previous supervisor (a bit of a charicature of a micromanager) did request weekly reports. His primary justification is it helps us come performance review time and provides some transparency into what we are working on so info could be forwarded on to somebody who could help: also kinda gives a bit of a boost to show you actually did something in weeks where it doesn't feel that way... I didn't mind doing it.
Given the sensitive nature of some of the things I work on, there's a definite "need to know" applicability here, which is why the current guidance from my supervisor is "do not reply."