This sounds like a good idea, but it’s actually quite a bit more complicated than it sounds. Anything displayed on the front-end of a publicly-accessible website is available to anyone, so this would achieve nothing unless it also restricted what was displayed on the front-end.
In addition, media in the uploads folder is completely open to the public if they know the right URL, so this would require the creation of folders that are locked down on a per-user basis. This would actually be better accomplished by creating a new, secure (from anyone not logged in) uploads area and then creating folders within that on a per-user basis. Then there would need to be a mechanism to detect who has access.
I have actually created such a set of folders for user-uploaded avatars and downloadable e-books, and it works well. But I think that (for the moment at least) it’s best left as plugin territory for those who need it — at least until we have decided what we’re going to do about the media uploads folder more generally.