It's how banks the 20th century worked with external systems (people in this case), I bet they were transactional internally once they were computerized.
In the 21st century, if I buy something at a shop and there are not sufficient funds in my account the transaction is canceled and I walk out of the shop empty handed. The non-transactional system is still there as a fail over.
This is not true either. All modern POS systems have an offline mode. Have you ever tried to use your card and the employee says 'the machine is really slow today'? That's because the machine was offline, but your purchase still worked. In offline mode the POS will still authorize the purchase up to a certain amount, typically $75 (up to the store). Those charges are pushed through after the machine goes online. Yes, it's a failover, but the point is even the modern online system is still not atomic and has eventual consistency.
Legitimate purchases outnumber illegitimate purchases by a large factor. It makes sense to err on the side of legitimate purchases. If it were atomic you wouldn't have been able to make that offline purchase, even though you had the money. Since it's true in the majority of cases they let those go through, up to a certain risk factor (the $75 limit).
Except no. They are transactional in the small. But the system itself is still eventually consistent. There are just too many transaction that ends up with a false positive or a false negative.
Plus ebery you do a transaction, you have up to 60 days to cancel it. You will get your money before that.
In the 21st century, if I buy something at a shop and there are not sufficient funds in my account the transaction is canceled and I walk out of the shop empty handed. The non-transactional system is still there as a fail over.