You are correct in that today a computer system takes care of all the data records.
A few punches on a keyboard, hit enter and it’s recorded. Give the cash to the
employee and away they go. Maybe a couple minutes at most.
Obviously you’ve never done payroll for a business. There’s a lot more to it than punching a few buttons and then bingo - they get a check! There’s a bunch of record keeping so that Uncle Sam gets his cut and the state you’re in gets there’s etc. I know, because I’m a bookkeeper and I do it for the business I work for.