Those "rewards/cashback" that we get are basically extra cost charged, passed back to the consumers as incentives since the issuing bank takes a major cut of the MDR. We are paying for those rewards that we can do without.
There are still some major barriers to mainstream adoption that need to be iron out, like convenience (tap to pay vs scan QR code, cross border transactions etc). Since the only beneficiary of these new payment systems are the consumers and merchants, banks have no incentives to push for it and may in fact pushback against it. The change need to be initiated from the merchants, especially the major ones and currently, the acquiring banks have lower MDR/incentives for major merchants so I expect these banks to do all they can to hold on to the pie.
Whats happening to mobile payments in the next few years can give us an insight on the future adoption of stablecoins, since imo stablecoins have a much bigger barrier to overcome as it requires mainstream adoption of crypto wallets + crypto enabled payment interface. You also have the regulatory/money laundering aspect to take care of.