From a percentage perspectice, handling huge amounts of cash should be far more expensive; I know one of the operators over here in my country: If you are a supermarket chain and have three locations in one large street, they charge you for every stop a minimum fee + additional handling costs.

When I suggested pricing like that might work, my point was not that it'd be cheaper. I 100% agree it'd be more expensive. But if it attracts a sufficient amount of additional business from people who want to pay cash it could still be a net gain (assuming those customers are still profitable).