Some people simply don't wish to be US citizens. Some countries do not allow people to hold dual citizenship (not sure of Italy).
My husband is Irish, and was a green card holder, with an American drivers license and an Irish passport until last year. He would never have applied for US citizenship prior to the 2016 election, and wouldn't have done so if Ireland did not allow its citizens to hold dual Irish/US citizenship. It's really not that big a deal, you have to renew your green card every ten years for a small fee. The trick is to not break the law, which as we've seen was nigh on impossible for Juicy Joe.