All modern cellphone systems are already digital, and the voice channel is heavily compressed using codecs that are typically geared for a human voice. It's pretty much impossible to get a high datarate with an acoustic modem over them, if you can even get a connection at all.

While there are higher bitrate codecs, a full-rate GSM channel is only about 13 kbps, and depending on radio conditions the voice data may be compressed down to half that or even less.

For comparisons, when landline connections are digitised, it is typically compressed to a 56kbps or 64kbps channel.

The cost of sending data over phone calls would be probably much much higher than sending SMS

Agreed it normally would be more expensive. Although I'm on a plan that gives me a few hundred minutes of talk time per month that I don't come anywhere near to using.