Every small business owner I've talked to in the US is either indifferent or prefers cash.
If [1], of which I've only skimmed the summary, shows that the EC was aiming to "calculate a level of interchange fee that makes the merchants, on average, indifferent between a transaction by cash or by card", and if that's the level that's been implemented in the EU, then they can probably call it a success.
In the last 3-4 years, I've been surprised a few times when small businesses (plumber, street food seller, dry cleaner) have preferred a card.
[1] http://ec.europa.eu/competition/sectors/financial_services/d...
Hiring those armoured vans to move it around, loss by theft or error by staff, time spent counting money, making cash deposits or withdrawals from the bank, and perhaps higher insurance.
Whether those costs are more or less than cash presumably varies. A public transport operator seems the obvious case where cash costs are high.
The EU capped fees at 0.2% for debit card transactions, and 0.3% for credit cards. I'd guess that makes them very competitive with cash -- the discount German supermarkets, well-known previously for only accepting cash, started to take cards. It also led to the demise of cashback credit cards, but I'm not sorry to see them go.
http://europa.eu/rapid/press-release_MEMO-16-2162_en.htm