I have removed my CC information after the registration process was completed. I had it on there for years and then there became too many instances of iTunes accounts being hacked and my family shares an account. When my kids started downloading lots (they are good kids and it was all free things that my wife authorized), I became leary that they might have somehow gotten the password and removed payment information to make sure they don't download expensive/ paid stuff (and will just add it back or used prepaid cards as I need them from now on).
The point of the post is to prove that it is possible to remove billing information and still have the account behave normally.