I think it's totally doable if you can avoid cash completely, but for most of the costs of handling it, they hit when you take your first dollar. If you're already buying a cash register, counting, making change, stocking cash/change, making a trip to the bank, etc., the incremental costs of additional cash transactions are minimal. Even with steps up for things like time-locked safes or pickups by armored cars.
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.