It might have something to do with the high fidelity voice calling having a reasonably large bandwidth that you could theoretically use as a data channel - many times larger than an old v.92 modem. Maybe that's not so relevant these days with more people having unlimited data plans.
(And in any case, as you suggest most people pay more per bit transmitted on a mobile voice call than they pay per bit as data.)
Purely for fun, it would be interesting to hack up two smart phones to transmit data over a voice call. Presumably, you can keep everything binary, if you control the end-points.
SMS is transmitted over digital signaling or transport channels. There was never any analog coding involved (except for a few retrofitted implementations on landlines in Europe).
