But it's more than just convenience. It's also the impersonal part of the text that makes it so popular. You can write stuff in text messages that would be wierd saying out loud.
Just like me writing this message to you - I can think about what I am writing, revise it, etc.
But, text messaging is considerate to the receiver, as it lets the receiver consume the message at their own time, while a call would have to interrupt the person whatever they are doing.
Text is better in very noisy environments, bars/clubs/concerts.
In Europe at least, texting as always been a little bit cheaper than a phone call, and the receiver usually doesn't pay for received messages.