There is a good bit of discussion on the costs of handling cash, which is a huge problem for some companies, for example those in the mass transit industry. However, most merchants in traditional retail businesses see things differently. This quote jumped out at me:
"For the retail grocery sector, Hammonds (FMI) argued that the current structure of interchange fees is an obstacle to wider merchant acceptance of electronic payments. FMI studies of the grocery industry show that today, the relative cost of accepting a cash payment versus a card payment favors cash. He noted that merchants pay bulk deposit fees to their banks for the cost of processing cash deposits. Because these fees have no relationship to the number of cash tenders the merchant receives in a day, these bulk deposit fees represent a fixed cost and impose no marginal cost. In contrast, Hammonds said, individual fees are imposed on each credit or debit card transaction, imparting a marginal cost to the merchant. Thus, abstracting from other costs, card fees pose a higher marginal cost to merchants for each transaction."
So for most merchants, cutting the amount of cash going through the tills will not cut the costs of handling cash. The card industry's promise of reducing cash handling falls flat with most of these types of merchants. Better to focus on all the other benefits that cards provide.