What I'm wondering is: why punch cards instead of paper tape?
Because it was already there?
Early commercial computers were made to replace tabulating machines. To do so they had of course to be able to read (and write) punch cards. There was no need for paper tapes.
Well, ok, paper tape was first, as the Zuse machines used them and some other experimental and scientific machines. Or not, as that was the time of primordial soup. Later on it was definitely only a thing for money strapped institutions. The real world revolves around business and business was all about card tabulating. That was were the money was the computer manufacturers were going for. That was were the computers were sold to. And that was were programs (and programmers) were needed.
So while there many good arguments can be made for punch cards (and I'd usually be first to do so) the real reason is way more mundane:
They used what was already available: Punch cards
It is never about what was invented first, but what environment a new technology is placed in. Existing data processing sites - the major early customers - had already everything needed for card handling, from keypunches over boxes and shelf for cards all the way to stand alone sorters and printers. That's everything needed to handle programming sans the compiler. Call it the IDE of the 1960s.
It as well helps to look at the contemporary landscape. Of the most successful computer line in history, the IBM/360, the most successful type was the plain Model 20. No floating point, no 32 bit, not even a full register set. By default delivered without tapes or disks (*1), but an all in one card processing unit, the 2560 Multi-Function Card Machine. It could handle the tasks of a reader, puncher, sorter and interpreter at once.
So, why would anyone introduce paper tapes to that world, making introduction of computers even more costly by requiring secondary investment in punch tape machinery?
Is that Sample Really Representative?
Users becoming time slots and setting up the computer on their own? Serious? It would be an extrem inefficient organization. I never have seen or heard of any computer shop set up like that.
Users normally never had direct contact to the computer. That was what the operator team was for. They were the guys - well, mostly gals - that carried the stacks of cards and paper around, feeding the machine to run with no slack between jobs.
Users would deliver their card stack together with a form describing what their input is / how it's supposed to be handled and what they expect as delivery of that job. This would be delivered to a counter outside the computing center - users never enter that place. It would be put in a box (if not already in one) and queued up with all other jobs.
Usually it was as well possible to send that job to be processed via in house mail (no, not Email, real mail, some guy pushing a cart), wich more often than not would also used to deliver output (and stack if that mark was set) back to each office.
In addition jobs could be stored at the computing center so only a form was to be mailed, stating which job is to be run at what data. Result would show up right at your office desk the next morning when the mail guy does his next round.
Plus them managing recurring jobs on their own. Just send a form (and a job) and mark it to be executed every day, week or month and you'll get the results without any further interaction delivered by mail.
Data processing is all about organization.
Computers just speed it up.
*1 - Which were only introduced later on and needed lots of RAM for system software, i.e. 8 KiB minimum :))