Italian is actually one of the more distant Romance languages of Latin, if I recall correctly. Its really descended from the dialect they spoke in Florence in the 14th century.You could say that Italian IS modern Latin.
Is modern demotika Greek any closer to classical Greek than Italian is to Latin? (I really don't know.) If classical Greek had given rise to half a dozen major modern languages, we might well call modern Greek 'Romaic,' or some such and regard it as just one of several Hellenic languages.