I use my Italian passport having found out I was eligible for one just 3 years ago and have never had any problems or been asked any questions except once when I was travelling with someone who I was sponsoring (but that was a unique situation I think!)
I don't think they can really ask an EU citizen questions if they are exercising their right to freedom of movement, I have also just used my Italian ID card to travel instead of a passport and that has always been just fine as well. As others have mentioned, your only problem is if you wanted to go back to the States you might not be able to go back very easily, if at all, and might want to look at legal advice for that situation.