I still have to pay the higher transaction costs even without a credit card, because the credit card companies require that vendors have the same prices for card or cash, resulting in higher prices for everyone.
You'll see cash discounts at some gas stations, and the occasional small coffee shop or takeout place will have a $10 minimum, but otherwise it's gonna be the same price most places.
Then it's nothing like taxation and it is optional.
The card companies charge merchants for transactions. The merchants raise their prices to cover those transaction costs: For a very long time (and still, in a few places) it was against the card company's terms of service to have a card usage surcharge. A very few places now have 'cash discounts' or don't accept cards at all, but these are by far the exception. As a result, /everyone/ ends up paying for credit card rewards, even those who don't use credit cards.