Here's how I think about it: Apple is the user's broker and Stripe is the merchant's broker. Every time there's a transaction between the user and the merchant, they are setting up a deal between their respective brokers.

As fgblanch points out, a merchant using Stripe only needs a single account with them to handle credit cards, Apple Pay, and whatever else comes along tomorrow.

As Igglybook and zaidf point out, Apple wants to provide the hardware and software for the user, but they don't actually want to be a financial services company like Stripe.