On the face of it, this is done to avoid confusion with other peoples of the American continent, north and south. But in my vast experience the people who use it most have an ideological ax to grind, which is not at all uncommon in Italy. The use of the unlovely statunitense (Unitedstateser) serves as a reminder that we in the United States are not the only Americans. This is true, as we can see by the endless flow of other Americans entering the US daily. And it serves as a reminder that we are no more important or influential than other inhabitants of the hemisphere. This is simply not true. As a nation, we are more important or influential and it is simply wishful thinking to deny this. Not (necessarily) better: more powerful.
Other things to remember about the related language aspects: americano, like all other nationalities and languages, is lower-case. The plural is gli americani, or gli statunitensi, if you must. The abbreviation of "gli Stati Uniti" is "gli USA," because "United States" is plural (as it once was here, until the nineteenth century.) The country name thus takes a plural verb in Italian.
