Credit card processors and airlines did millions of transactions a day in the 1970s, and they managed it with CICS.

It sounds like you have no idea how credit card transactions were or are processed. They are almost exclusively file and batched once a day, even today. Back in the 1970s it was even worse because there was no real time authorization.

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He or she is correct that the cash settlements were and are batched, but authorizations, reservations etc were online - to the mainframe that's just another transaction.

The reason settlements were batched was to save on wire fees.