My biggest motivation for requiring weekly status updates is that in the past years I had a hard time following the GSoC projects I was not involved with directly. At WorldForge, we required weekly reports to the mentor at first and then decided that the weekly reports should go to the developer mailing list. That kept everybody informed what was going on.
I would say this seems sensible - the weekly reports would not necessarily have to be greatly detailed, but I imagine it would help to keep students on track, and would enable the rest of the community to know what's going on with the students. From experience, I would say that I probably only tended to post on the lists when I had specific problems, or patches to submit, so a weekly update would have likely resulted in more interaction.
Cheers,