Is it true top tier customer reward cards (black/platinum/amex business/etc) have interchange fees that push into 3% territory? If so, how do companies like Square make money when they only charge the merchant 2.6% for a POS transaction?
Corporate cards actually earn significantly higher interchange, but even those don't aggregate out above 3%. Actually, the networks spend a lot of time policing banks from trying to arbitrage the difference by issuing corporate cards to individuals.
Payment processors like Square just know that their margins will vary by the type of card used by consumers, but aim to have an aggregate positive margin across all cards. Once you get into enterprise contract negotiations with them though, they'll look at your card mix to make a pricing offer.