I'm very sympathetic to both the cash-as-privacy and cash-as-fair-access (for unbanked people, to goods and services) arguments, and I won't support any business that doesn't take cash.
Credit cards are a snare for the chronically indebted, to shake pennies from their pockets to transfer to the wealthy.
However, if you have no debt (which is enough to be considered "wealthy", IMO), you'd be a fool not to use a credit card for most transactions. Because the rewards they hand out are built into the prices paid for everything by people who pay with cash.
In my own case... I got my first credit card at 18, and by the time I was 22 I had racked up $20k in debt. I took drastic action and stopped using cards completely, and lived only on my income from multiple jobs, going without anything I wanted to buy for several years. Beans, rice, pasta, one pair of shoes, three shirts. Until I paid it off. By the time I was 24 I had paid it off waiting tables, driving taxi. Then I cancelled my cards. And so for reasons unrelated to privacy, I had no credit cards for 15 years after that, and only used cash or debit cards.
It was only in my mid thirties that I was put wise to the fact that I was losing 1% to 3% of my average spend by not having a card. So I got the most expensive card I could with the best payback ratio, and have never carried a balance on it at the end of a month. Over the ten years I've had it, it's paid me back somewhere around $30k, all siphoned from the pockets of people who don't pay their debt off.
Is this a vile and rapacious system? Absolutely. Would I be stupid not to take advantage of it after doing my time and learning the hard way? Yeah.
I still pay cash a lot, because I don't need a record of what I'm up to. And I'd support a ban on credit cards which would lead to merchants dropping prices for everyone. But here we are.