Assuming this is true, and these anti-steering provisions prevent merchants from discriminating, what prevents Visa from issuing cards with 200% fees? What's holding the cash back level at a mere 1-2%?
I believe Amex is only able to get away with its highest-in-the-industry rates because of the association of Amex cards with business expense accounts and high income earners. This is changing now (https://www.ft.com/content/715d785e-23fc-11e8-ae48-60d3531b7...) especially after years of competition from banks like Chase, who have been working on creating what is essentially a structural clone of American Express’ network (https://www.reuters.com/article/us-jpmorganchase-creditcards...).
Here is one example from Australia, where 15 years ago I worked on credit card pricing and product design...
When Platinum cards were introduced to Australia, the banks agreed to a high interchange rate for Platinum and an offsetting reduction in interchange on other cards. I forget the exact interchange rates; they were on the order of 150bp (1.5%) and 50bp, giving a weighted average around the then regulatory cap of 65bp.
My bank was ready for this, so we moved most of our high-spending customers to Platinum ("in recognition of their status") and reaped a windfall from the higher interchange. Part of that was used to fund more loyalty rewards on Platinum. But most was pure profit...
Over time, regulators got wise to this, and reduced the overall interchange rates to the minimum (possibly 35bp in Australia now). Essentially in Australia it is enough to covers the scheme running costs and disputes/fraud. Loyalty has to be funded in other ways (annual fees, cross-subsidies from other customer revenue, points caps, reduce value of points, making it harder for customers to redeem points, etc).
This means customers in shops are no longer paying the cost of loyalty schemes even if they pay with cash.
(Amex operates under slightly different rules from Visa and MasterCard because the legal relationship between the merchant, scheme, issuing and acquiring banks and customer is not the same. That is why Amex can often offer better rewards that Visa/MC in regulated markets like Australia, UK and Europe)
They charge what they can get away with, and generally they can, or rather could, get away with the higher rates. A couple of percentage points was worth it if it made the sale, especially if there was a high likelihood that your customer only had that one method of payment. Now almost everyone has multiple cards, and many retailers are pushed to much lower margins, so we see the results that we see.