Nitpick - iMessage is also Internet-based. The phone number is only checked once when you first install the phone (by Apple sending an SMS that the OS intercepts) and is then registered with Apple so that other Apple phones with iMessage enabled know that this number can receive iMessage. The carrier is no longer involved beyond the initial verification step.

You can also use iMessage with an Apple ID, including to contact those who only have a phone number (and the reverse also works). This works on non-cellular devices as well such as iPod/iPad/Mac.