I've felt this struggle from the other side working at a gas station attendant. We were only allowed to have $100 before the till made us dump it.
Can you break this $100 bill? Maybe if you pump another $50 in fuel, unless you want this roll of quarters too.
this is false reasoning on their part. They never have thought about how much cash costs them so it looks like extra money but it really isn't. they need to count the time lost to counting the cash as you pay, then the time to count the money in the till at the end of the shift. Each count above is 2 counts at best the average is closer to 3 because you sometimes get it wrong. There is also theft costs which is generally ignored but a real problem.
credit cards is money right to the computer which is not only fast it makes less mistakes.
That said, while I default to using Apple Pay for basically...everything, I too do not wish to live in a society where large companies get to govern every transaction I make. Or, for that matter, every transaction I make being on a ledger that the government can monitor.
Do they? Unless the shop's always serving customers, this may be free time.
You also completely discounted the managers time counting cash in the backroom. That is more than an hours work in my experience, time that could be used for other things.
Many of my cash transactions are approximately as fast as or even faster than card transactions.
Because tax evasion? Otherwise credit card interchange rates are nowhere that high, typically 3%.
Potentially ranging from 4.7% to over 15%, costs include labor for counting change, closing drawers, preparing deposits, security expenses like armored transport, bank fees for cash services, insuring against significant risks of theft and fraud.
In the end: fairly unimportant... except for that perceived "cost".