Mobile phones need charging and connectivity. As has been pointed out, existing landlines are powered by the exchange and so you can have a traditional phone that works whenever the circuit to the exchange is (mostly) working. In particular, a dodgy connection in the circuit probably still allows an analog phone to work (though it will sound crackly), but there is no chance of running data over the same circuit. This is based on my experience at my 98 year old mother's house where, whenever it rained, the internet would drop out and the phone line would be crackly. By the time that the BT person came by, it had stopped raining and they went away with "problem solved".

Now, I guess it would be possible to power the ATA from the network, but I doubt that that will happen.