ANother one here who likes text messaging but hardly EVER uses the mobile phoens for voice calls, as it is teribly expensivie in my case - worthwhile if very important, but otherwise not good for penniless Celyns.
I think all my reasons have been convered by others, although I am not sure if anyone included my own cynical one - namely, that it lets me send a quick message without getting into a tedious 20 minute chat about it. Cheaper and less hassle. TImes when an interactive onversation is need, fine , that is what I do.
Sadly, I cannot deal with my parents that way, 'cos they have not really worked out how to do it. 
It lets me notify someone of a change in plan - “running 10 mins late” etc.
It lets me send a quick message to my brother or whoever - someone who might be in a car, and therefore absolutely not able to take a call, but quite able to think “Oh a text from Celyn - OK, I’ll get that in a minute when I can park”. (IT is now illlegal in the U.K. to use a cellphone while the car engine is running - one must have the vehicle stopped and engine switched off.)
In terms of getting a short message across, it is cheaper, and as others say, less intrusive, than making a call. I would hate to be the “I’m on the train” talking-out-loud person, but I have sometimes been terribly pleased that I can simply send “sorry - busses all to hell - train instead. ETA xxxx” .MInimal disruption for me, for other passengers, contact maintained with the poor fool who is expecting me by bus.
I don’t, however, use it for any of the supposedly useful servies - weather, sports results and so on.
It is, though, tiresome to type n a tiny little alphabetical “keyboard” - but mostly worth it.