If you look around for riot posts at the beginning S3 they talked about a few reasons for hiding elo:
1) to prevent abuse and bullying based on someone's visible elo (OH YOU HAVE A 1300 Y U SO SCRUB)
2) As someone said before, it prevents people from reaching a certain elo and then never playing again (SEE I DID IT)
3) Visible progress and rewards, and you get to keep your League regardless (this is related to #2, but the tangible carrot of being SO CLOSE to the next tier is something that makes humans go WANT)