The thing is reward credit cards really feel like the banks are fleecing merchants and giving a small portion as a kick back to the consumer. If card issuers want to provide an incentive to their customers then they shouldn’t fund it by charging the merchants more.
All that will likely happen is merchants will increase their prices and those without reward cards will end up paying more and getting less. It’s probably why on so many sites (especially airlines!) I have to pay ‘2% credit card processing surcharge’.
If Visa and Mastercard don’t want retailers to get selective then there needs to be a single charge rate - and I think it would be a good idea that this information is shared with purchasers at time of a payment.