But Visa and Mastercard effectively set the rates, and the higher they are, the more issuer business they get; meanwhile merchants are essentially never in a position to reject either Visa or Mastercard (notable exception Costco confirming the general rule), so market forces are pretty one-sided.

I think if Visa and Mastercard were three-party networks like Amex or Discover (now Capital One), their interchange would have long been regulated down by >90%.

French companies pay social contributions (~45% of the full salary) via Visa and MasterCard, and the French authorities are making it nearly impossible to pay these by wire transfer.