Apple Pay and Google Pay are not payment networks. Those are just Visa and Mastercard.

It depends on your payment gateway. I can setup a POS payment system with any payment gateway processor I want. Depending on the system you can essentially run direct deposit into Google Pay, and as a vendor I can direct deposit the money into my checking via my gateway.

But that's not the issue being contested because there are hundreds of payment gateway processors available.

Right, you CAN set that up, but in the US, not accepting visa and Mastercard is essentially untenable if you are a retailer or restaurant. You might be able to avoid accepting AmEx, but from talking with restaurant owners, the biggest spenders are often AmEx holders and are annoyed at having to use a backup card.

That's not how the payment market works, though.

If a customer walks into your store and has exactly one (type of) card on them that they want to use to pay, you have a choice of accepting that card or losing their business.

This makes competition between payment methods at the POS structurally very hard.

Which of those is realistic though. They exist but you turn away customers with money who cannot pay.