How would you guarantee responsiveness? With a voice call, the representative is on the line with you until your problem is resolved. With a text message, the rep would have to start helping somebody else if you took too long to reply, and may not be able to get back to you for a long time. Since they have no way of knowing how soon you'll reply, or if you'll reply at all, they can't just sit there idly waiting for your reply for a couple of minutes. And if a rep gets a large number of slow repliers queued up at once, he'd have to mentally juggle several different conversations and couldn't give any of them his full attention. Which caller gets priority? The one who you're currently texting with or the one who just came back after five minutes? What if a caller hasn't replied for a while and it's the end of the rep's shift?
Also, is there any way to route text messages through a call center so that a caller could text a single customer support number instead of having to know the number of the next available service representative?
One more thing: SMS messages get lost at a rate of 1 to 5%[1], so you're going to have a lot of irate customers wondering why they never received a reply. If a voice call drops, both sides know about it immediately.