Text messages are sent in the signaling channel, this is the channel that tells your cell phone it has a call and other stuff interesting only to telephones. The advantage here is your phone is always listening to that channel.
SMS is sent during idle spots in that channel, but it is a very limited channel and you couldn't run large amounts of data through it, there just isn't enough idle time.
Scarce idle time sounds oxymoronic, but it is only idle in the sense that it isn't connecting and disconnecting phone calls.