They care because they must pay a 1% fee to the issuing bank for each transaction. c2it appears to be eating this cost, hoping to make it up on the float in certain cases or in other ways, some of which may not yet be revealed. That is, perhaps they are trying the old dot com trick of capturing market share first, and figuring out what to do with it later.

The reason they must pay a 1% fee is that they are submitting the transaction as a purchase. The fact that some card issuers are treating these as cash advances is a separate matter, and is covered in other threads.

It is true that the issuing bank is responsible for buying the miles from the airline, but this is covered by the 1% fee they receive from c2it. It's true that c2it pays the 1% fee whether or not there's a mileage card involved, but only a mileage card is going to create the huge incentive to route funds over and over in a circular manner. Non-abusive uses of c2it are unlikely to generate huge amounts of transactions that won't lead to further loyalty.