You're making a generalization here that is not true. Some systems may work this way, but many do not. For example, here in the NYC area, the large cable network Cablevision, only supplies a VOIP box that the customer plugs into the cable and AC supply anywhere inside their home. If the power goes out, there is no cable feed powering the box and you lose service.
Plus, many people are using third party VOIP phone services, like Vonage. They are not even part of the cable or phone companies. They send you a VOIP box that is also powered by the home AC.