Apple has said they'll be charging zero interest and zero fees for this service, including zero late fees, so where the yield will be coming from is unclear. That said, I confess that I don't have a deep understanding of the BNPL market.
With respect to cards: cards have a number of advantages for both merchants and customers. Cash is not free to handle and carries risk (theft, etc) and it's really slow. Credit card buyers tend to have larger average ticket sizes (20% larger was the last one I saw) and card buyers have more confidence buying from smaller shops knowing that they can always charge back the merchant if something goes terribly wrong. In a real way chargebacks are a big part of how we got e-commerce.
Merchant agreements generally precluded credit surcharges but they always allowed cash discounts. This is commonly seen at US gas stations to this day. They also prohibited credit card minimum purchase amounts. To my knowledge both of these are no longer true.
Shops aren't putting up with cards so much as embracing them because that's how their customers want to pay, and they don't want to miss out on a sale.
For what it's worth I think BNPL is simply an attempt by Apple to get some yield on their insane cash pile. Last year they had over $0.2T on hand. [1] They're making it faster than they seem to be able to return it to shareholders.
BNPL is a pretty bad business - margins are low, buyers are generally not qualified in the same way as other lending, ticket sizes are low, and collections aren't worth it (you really gonna repossess my $20 gently-used socks?). However, if Apple has a better way to qualify the customers (a big if)...
They can take ~3-4% of the transaction, net like 0.5% for a 6 week loan, which is like a 4.5% APR. Their margins may be better than peers since they can use their own cash instead of raising debt. Maybe 6-7% APR. It's also short-term debt that turns over fast so it's highly liquid.
My wholly uninformed opinion is that this is more of a cash management product that happens to be built on their data for Apple than a data product per se. After all you can't just roll up at BofA with a $0.2T check and get that kind of APR.
[1] https://www.investors.com/etfs-and-funds/sectors/sp500-every...