Non-transferable tokens would not be traded on the open market, since they're meant to be used directly from one peer to another. Just like loyalty points work today (where you can only earn or redeem points from an specific business), non-transferable tokens would work the same way on the Blockchain. It could be complicated to restrict transactions to a single entity, but I believe that something like this could be coded on a smart contract.
Given that the Ethereum platform is not scalable yet for mainstream use, I'm guessing that mainstream businesses and companies will launch their own non-transferable tokens on other chains like EOS and TRON. Speed and low costs are of the essence here, to provide a rewards/loyalty program to everyday customers. It's more secure to do this on the Blockchain, than any other way. If there's enough interest/demand for something like this in the future, you could expect Burger King, Autozone, and other major stores/retailers offering their rewards program right on the Blockchain. It will greatly reduce fraud, as points will be directly linked to a customer's identity on an immutable Blockchain network.
Whenever we'll see this become a reality in the future, it's yet to be seen. At least, we have token standards that make issuing securities on the ETH blockchain a lot easier than we've imagined. It's possible that the "freeze" function can be modified to the developer's content, in order to create non-transferable tokens on the Blockchain. With the ever-increasing popularity of Ethereum and other smart contract platforms in the mainstream world, I believe anything is possible. Just my thoughts