I was in Rome last September for a few days before my Sicily trip, stayed in a well known hotel across from the Vatican, and found both restaurants and even the cell phone company "ORANGE" refusing to take credit cards! The hotel also 'pressured' to pay in cash, offering a discount (not much) for cash. I refused this offer. It seemed very unusual to me, as this was my sixth trip to Italy. I have friends in Sicily, and they thought maybe it was because of taxes (?)
I, also, have never, in 40 years not paid off my credit cards monthly, and in the US I use my skymiles card to pay for everything, including groceries. I expected to pay for small purchases, panini, pizza, taxis, etc with cash, but last year felt 'pressure' to pay for larger purchases in cash. I will advise you to make sure you have cash euro on hand, and make sure your home bank/credit union debit card knows you are in Italy and will be withdrawing money in Italy. You will need more cash there than here in the U.S.
Italy is not the US, and the reason I travel is to experience the differences, even sometimes, the inconvenieinces! If I wanted a US experience, I'd just stay here. I enjoy all my travels, but especially my Italian adventures.
Roberto! Feel free to chime in if you have a response on this, and any reasons you can think of for the demands for cash from the Roman businesses.