Credit card rewards are just discounts, discounts that are charged to the merchant. It's not a free lunch by any means.

And as a merchant, yes it's annoying, but it's also nice when a customer pays with a credit card, because we actually get paid then.

I think that's a technicality. From my perspective 100% discount is called "Free", and I get that a few times a year when flying (tickets, upgrades, etc)

I calculate 100% based on the amount I get from my preferred airline for paying cash for groceries (0) vs the amount I get by using a card they issue (a few imaginary points/$). Then I trade those points for things I couldn't have had by paying cash. As long as I don't pay interest, we're in "Free" territory.

No, you’re still paying for all of that to some extent. Less than people carrying a balance and/or paying with cash or debit cards, sure, but more than zero. (It would be a pure redistribution from cash to card payers only if issuers made no profit or even a loss on never-balance-carrying cardholders, but if they didn’t, why would they still have them as customers?)

It’s still the rational thing to do from an individual perspective, of course, which is why these rewards are so sticky.