Universities typically have all rights to their students' papers. I'm not sure that I'd expect privacy for college essays either, although it's a bit odd that you are technically not usually allowed to, say, post them to your blog.
Do you have any sources for the claim that universities typically have all rights to a student's papers? I can say for certain that I never signed any intellectual property agreement with the university I attended and would expect to retain all rights to any work I completed there as a student. The work I created did have an implied license allowing for grading the papers and such, but any use beyond that would upset me unless I the university had obtained my permission.
Not sure on what's typical, but my University uses a "you get to keep your IP" as a selling point; so presumably there must be enough of other institutions where this is not the case. UMissouri's attempt to claim royalties for student's in-class developed iPhone app (although later backing down and changing policies) is an interesting example of the other extreme.
