We don't use any cards for online shopping, what do you mean? In most European countries online shopping uses a payment API that takes you to your bank's payment portal where you can review the transaction amount before confirming. It's no longer the 20th century, we're not handing out any card details to online merchants.
Banking in the US feels like it's stuck in the 90s. Heck, half the time, it's not even chip+PIN, it's chip+signature (which is a relativelyrecent change from carbon copy or swipe and signature).
I've never had a web shop use an API to deduct from my bank account - the closest thing is PayPal, which as far as I can tell is basically ACH under the covers, just though an intermediary. Pretty sure more Americans use their CC or debit card for online shopping.
Of course all online merchants in Europe take card payment. Some of them also offer payment by bank payment portals, such as you've described. These have zero benefits for the customer.