If the airlines' sole business is to fly people around, there would be no rewards. Clearly their business is not only to fly people around, but to make it so that people prefer to fly around. Moreover, they still fly people around who redeem award tickets paid for with miles earned from affinity cards.

Or let me put it another way. The frequent flyer program of nearly every airline is actually a separate company. In most cases, it's a wholly-owned subsidiary of the airline, but it's managed entirely separately from the flying operations part of the company. Some airlines have actually spun off their FF programs into entirely separate companies, i.e. not subsidiaries. In other words, the airline is still entirely in the business of flying people around, although they allow people to pay with miles from an FF program instead of paying with cash. It is the FF programs, not the airlines specifically, that allow people to accrue miles for things other than flying. (Perhaps this is an academic point since, as mentioned, most FF programs are wholly owned by their parent airline... but IMHO it's an important distinction.)

Regardless, my point is that airlines don't have to offer any rewards. They offer them as perks for loyalty, sure, but they got along just fine 30 years ago without any FF programs. (In fact, they were probably better off back then.) In today's market, they offer FF programs to remain competitive with consumers who demand to get everything for nothing. Part of that includes offering miles for things other than flying, but the airline makes money off of that, too.

Remember that the airlines are in the business of making money, not of adhering to one and only one business model. If you don't like the way a particular airline conducts its business, the best remedy is to vote with your wallet and find an airline whose business meets with your approval.