I have no numbers, so it could be totally off-base, but it feels not-impossible that it costs a percentage or two to process all your cash anyway, so the difference between cash & credit cards isn't actually that big. It's just that the interchange fees show up as one big chunk whereas the cash processing is lots of little bites, or even accounting for things that didn't happen (like skimming).
I guess this only applies if you're legitimately reporting all your cash take, if the business itself is skimming for tax reasons then the savings on cash would be substantial.