It's an interesting idea. It could be implemented in the future with many different cryptos, not just BCH (although as far as I know, for now, BCH is the only one offering this SMS feature, which is admittedly kinda cool). It could catch on in regions where people can text, but do not have internet access.
The thing is, BCH offers nothing truly unique over a huge range of cheap, fast cryptos. I could use Dogecoin, for example, to accomplish pretty much anything that BCH offers.
The difference with BTC is its hashing power, security, decentralization (not as decentralized as some other currencies like Vertcoin), widespread adoption, and authenticity. I just don't see those characteristics in BCH.