That’s not true at all, particularly for large purchases.
If I go to an electronics and check out with $5000 in electronics, there’s no way that handling cash incurs the same expense to the store as the 3% fee ($150).
Maybe for nickel and dime purchases, but that’s rarely the case.
Even a $50 dinner doesn’t cost the restaurant $1.50 (plus the $0.30 transaction fee) just to handle cash.