Funniest is that nowadays card payments are likely cheaper to process for merchants than cash - if you account properly for all costs. So credit card companies should start lobbying to allow different pricing based on payment methods.
If I'd start a small business, I would flat out refuse to take cash. (in Europe)
I agree with the sentiment, though. I guess realistically if it were my business, I'd need some significant evidence that I wouldn't be losing money by not accepting cash. That's the extraordinary claim, after all, with the vast majority of businesses doing it.
I think I've seen a few food trucks in my area that don't take cash.