Right. If a rep is sitting around just waiting for the customer to finish typing, then that is very inefficient. I would think they should be handling multiple chats at the same time.
His responses should require minimal interaction. His first couple responses should either be completely automated, or at least copy/pasted. He should also have multiple troubleshooting steps and solutions ready to be pasted into the chat window. And, hopefully, his chat application should be able to at least paste images, which would really help guide the customer through the steps.
Further, the OP seems to forget how many times that either he or the customer has to repeat himself on the phone because he couldn't understand. Plus, you can't just fire off 5 steps for the customer to take at once while on the phone, like you can in chat. You have to wait until the customer is done with each step before moving on the next. And, of course, you can only talk to one customer at a time on the phone. A chat rep should be handling multiple cases at a time.