Well, they're doing it, and there are (at least, that we know of) 8 US military bases and over 11k US military personnel on Italian soil, they killed civilians with impunity more than one time.

For example: https://en.m.wikipedia.org/wiki/1998_Cavalese_cable_car_crash

They're usually tried in US courts where they're handed a slap on the wrist and Italian courts can't do anything about it.