They can barely respond to emails in a timely fashion - I can't imagine that SMS messages would be any better. Not to mention the potential issues with trying to decipher a ? that is only 160 characters long and replying in the same amount of space. Maybe it could work for basic stuff like flight status, but nothing more complicated, I think.
And I don't bother with text messages, so not everyone would benefit from it, though as noted above many folks do receive their alerts that way.