This is not true. Transaction volume for consumer banking, even including credit card processing, is minuscule - a heavy customer might generate a half-dozen transactions over the course of a day, and many of those (particularly credit card transactions) are able to be asynchronously processed over the course of days or weeks.
Ultimately banks are in the business of money management, not money tracking and have been for the 700 or so years they've been around in recognizable form.
Whether they could do this with less overhead than they presently do with new technology is a separate issue.