Usually, a product that costs $100 costs me the same $100 regardless of the payment processors involved (and $100 cash when none are involved), so I can't see where "lower prices for consumers" could come from.
So I assume that if they were accepting more expensive cards, they might've increase the price of the $100.16 product for me, to offset their costs.
And yes, I also heard that payment processors have rules that require merchants to have the same price no matter what payment processor (or cash) customer will choose.
Alternatively, merchants can give users more cashback points for using their preferred way of paying. Not sure how this flies with payment processor rules, but I've seen it in the wild.
In this case, people who don't have local cheaper option won't be able to buy from them.
Cash/local-card-only might be OK for a grocery store in rural area only serving the locals, less so for a coffee shop in tourist centre of a major city.