Who says you even need cellular service? It's just a different type of radio signal, VoIP has existed for years. If you even need a phone number. Every app under the sun has a calling feature now, but most people don't use phone for calling anymore. Wifi is everywhere so cell signal is not as critical these days.
As a child, I was just not given home wi-fi password, and the cell plan effectively had no internet (to be fair, parents were on the same call-and-sms only plans as well). I definitely did not want internet bad enough to wander around in search of public wi-fi.