In the case of air travel where you're, presumably, going to travel either way, I think it can work out. But it only works out if you travel A LOT. Even a moderate amount of travel means you don't win out with the cost of membership.

Welcome to capitalism. Do you refuse to buy items on sale at the grocery store because they are subsidized by the more premium items? Do you refuse to buy the rotisserie chicken because it’s a loss-leader priced to get you into the door?

You’re taking a 2%+ loss on every purchase if you’re not playing the game. But you better carry debit cards and cash because some vendors charge extra for credit cards, and some charge extra for using cards at all!