The way I look at it, when you exchange cash for cash, you are actually buying cash. Whether you buy € here or over there with your $, the entity that sells the € needs to make a profit. It is not a free service.
As previously stated, you may not be able to find an Italian bank willing to buy your $ with € at all. You will be able to find bank ATMs easily, by far more easily than finding a toilet.
If you use an ATM to withdraw money, you are taking it out of your account. If you use a bank ATM in Italy to get €, you will not be charged by it unless you opt for DCC (Dynamic Currency Conversion). Don't do that!
Your home bank may charge you a variety of fees, so you need to find out about those, along with your daily withdrawal limit, when you inform your home bank that you'll be using your credit and debit cards in Italy.
Go here -- https://www.ricksteves.com/travel-tips/money -- for the full scoop on money in Europe.