If I understand it right, merchants often aren't allowed to pass on the fees or (much the same thing) give discounts if you chose a cheaper payment option. No wonder there's little competition on the fees, and Visa[1], Mastercard[2] and PayPal[3] are all having record profits.
[1] https://www.cnbc.com/2017/10/25/visa-quarterly-profit-rises-...
[2] https://www.reuters.com/article/us-mastercard-results/master...
[3] https://www.reuters.com/article/us-paypal-hldg-results/paypa...