> You shouldn't get a cash discount
Maybe, but "should" has nothing to do with it. Either I get one or I use my credit card.
> cash costs the merchant MORE than credit card fees
That's not my problem.
Just pay with a credit card, it's the optimal way by far (float, flexibility, rewards). No need to overthink it.
None of this is your problem: you are not a merchant. What is wrong is the analysis of various people who think cash is cheaper and thus get mad at not getting a cash discount. It is also wrong that a number of merchants are bad at accounting: they think that cash is cheaper by enough to be worth a discount - but this is not your problem either.