I quite like the idea as long as it doesn't mean consumers are incentivised to get rewards cards. Rewards cards are a scourge and should attract a mandatory surcharge to the customer over which the business has no control.
Why? Rewards cards shouldn't be a thing. They just increase the cost of doing business and all consumers are subsidising the card provider and their customers in the form of higher prices.
"No Amex" is a beautiful sign to see at businesses who refuse to play ball.
But the same should go for frequent flyer miles and the like.
All businesses ought to prefer EFTPOS because it's cheap as chips in comparison to visa and MasterCard, but the payment providers are making them artificially more expensive in some cases.