Sure, that's true so long as the reward system exists. But if the reward system didn't exist everybody (including YOU) would be better off.

I wish there was an economic expression to describe the situation with credit cards and their rewards. Tragedy of the commons[1] and the unscrupulous diner's dilemma[2] both come close, but aren't exactly right.

[1] https://en.wikipedia.org/wiki/Tragedy_of_the_commons

[2] https://en.wikipedia.org/wiki/Unscrupulous_diner%27s_dilemma