For example, a bank could offer partial rewards for using their payment system, over Apple's. The effect would be the same as passing on the savings to the consumer.
Given the software that banks generally produce, it’d have to be a sufficiently good reward. If I’m buying a $10 sandwich at a deli counter, I’m going to double tap my power button and tap my phone on the debit machine. A $0.03 cash back isn’t worth the hassle to fish around to find my bank’s app, enter a secure password, and then enter a 2FA code. I had another comment elsewhere in this thread: want me to use the bank app instead of Apple Pay? Make the bank app suck less.
There are ways to get around that.
For example, a bank could offer partial rewards for using their payment system, over Apple's. The effect would be the same as passing on the savings to the consumer.