This completely ignores that processing cash isn't free either. In Germany this is no longer a government paid process. Now at market price stores have to pay up to 50 cents to process 50 one cent coins.
One would think, however, that there would be little need for a store to process coins through a bank, as on average what's taken in as change on one purchase is returned to a different customer on another purchase.
This is echoed in small by the fact that I seldom have more than a dollar or two in coins in my pocket despite doing the bulk of my grocery shopping at WinCo* - sometimes I give exact change, sometimes I get coins back. My cash flow is occasionally getting a bunch of $20 bills from the ATM, which then dribble away in various-sized increments, never really accumulating more than a few bills or coins of any smaller denomination.
*The great thing(s) about WinCo isn't the prices, it's the number of things they have in bulk (did you even know there are a dozen types of flour, or 20 types of rice?), and that I don't have to listen to damned Muzak while I shop.