I don't think anyone's claiming otherwise, but I can count the number of times I've ever gotten a discount for paying in cash on the fingers of one hand, so I might as well do what's most convenient for me.
Most restaurants around here are locally owned, and I can't think of a single time they've charged me a different price for CC vs cash. I would imagine the vast majority of flea market sellers are doing it under the table, so it makes sense they'd only take cash. I don't do antique shops.
You don't say what your business is, so it's hard to draw any conclusions on how it works cash vs. cc.
You do bring up something I've always wondered about, and that is those cellphone ap "banks" like Chime, etc. The tv ads claim they don't charge any fees, so how do they make money?
Most of what I buy from mom & pop places is relatively inexpensive and just as easy to pay cash so I do. If it was buying something more than $100 or so (say an appliance) I'd use CC. I don't carry large amounts of cash.
I have never heard of a store owner (assuming you could track them down) who would open their store at an odd hour. What kind of "emergency" are you referring to?
The only exception is a neighbor (now retired) who ran an auto repair business out of his home. Often as not he was putzing around in his shop on a Sunday or in the evening anyway and would help out a customer. Even when he was still open, he was souring on the idea...too many people treating him as being open 24/7.