For those wondering why you can't use "anonymous" phones like prepaid or VOIP I can give some insight. Note these are my OPINIONS only.
I see two reasons. One is security and the other is legal.
1. Joe Everygamer is just doing his thing. He does not care about RMAH and never heard about password reuse. He gets compromised. The criminals attach a mobile Auth to his account, attach a stolen paypal, and attach an anonymous phone. They then start flooding the AH with items at prices they control. They would do it with many accounts which would affect the economy as a whole. It would also be terrible for poor Joe Everygamer who now has a bunch of fraud charges on his account and is banned.
2. The RMAH is region limited and some countries do not allow it at all such as China. One way to ensure that anyone cashing out is in the proper region is to use a valid and real cell phone before real money can be earned. Speculation here..but there may be legal requirement for this to help verify regions and countries.
It means that people from countries where it is banned will want to steal accounts from areas where it is allowed. Having a legit phone with an active plan in that area at least slows them down.
It's very simple. Text messaging is not SMS. Text messaging phones are not allowed by Blizzard for authentication. It has to be SMS.
The difference between text messaging and SMS is that text messaging simply means sending a text message to some device. That device could be your phone, your tablet, or even your computer. The sender has no way to verify what device received the message, nor where it was located.
VOIP has the same problem. It offers no location services. You can guess location from IP, but someone could be using a proxy so that renders it useless.
SMS is a very specific text protocol that is tied to geolocation services by your cell phone company. This enabled Blizzard to know that:
(1) The message was received by a cell phone whose owner is known by the cell phone company. They can match records of name/address if need be.
(2) That the recipient is located in North America, and is not some foreign farmer.