Hidden Profiles

Or perhaps EA is rooting for the other side, which buys their titles more often—when they're banned and forced to buy another copy of the game.

Why else would they hide it, especially when playing an online game?

I agree. All profiles should remain public. Not only is it a great way to check for potential cheaters, but if you receive a friend request from someone, you may want to check their profile to see if they'd make a worthy teammate or not before accepting it. There is no good reason to allow profiles to be hidden.