Public URLs can also be considered sensitive. Assume that there’s a site containing information about topics about how to handle certain diseases. Now someone pastes a link to an article on that site somewhere (forum, email) incorrectly, i.e. without the protocol. Another user sees it, copies it into her browser’s URL field and presses enter. The browser tries to connect via HTTP, and if the server accepts connections to port 80, the information that this person tries to read an article about a specific disease is send in plaintext over the internet.
If your solution to this problem is “don’t allow to link to individual articles on this website”, well, that’s not a solution. Closing port 80, on the other hand, is a very practical solution for this problem. (In fact, it’s the only solution I’m aware of which solves this problem.)