In most parts of the world, POTS is 64 kbit/s, over which you can reliably run a 56 kbit/s modem. Cell phone audio uses less bandwidth, but I can imagine that you could get 8 kbit/s or more reliably, compared to the SMS data rate (7 bits/char * 160 chars/msg * 3 msg/sec = 3.4 kbit/s).
I think you have a point, but note:
> The phone recieves this stream at a rate of 3 messages per second
So note that's 180 text messages a minute maximum throughput, not thousands.
I think you raise an interesting question of if it might be faster to implement a software modem over your voice connection, but I also have no idea if that's actually feasible or not.
(will various kinds of digital audio compression or filtering get in the way? I dunno. Can android apps easily get access to the voice audio stream in the way they'd need? I dunno.) (it'd certainly be a lot harder than letting the SMS network take care of the transmission layer, at any rate). (But yeah, if internet over SMS is a cool hack, then internet over software modem over audio would be even cooler!)
In the mid 1980s I used to load computer games onto my ZX Spectrum using analogue tapes and an old hifi. 1535 bit/s :)
Calling my number and using the good old dial-up method sounds much more efficient actually. Isn't the bitrate around 128kbps in normal calls?