I can't speak for the Greek situation as I'm not informed enough, but I'm Italian and I don't really agree that the Savoys were just a "convenient scapegoat". King Vittorio Emanuele III played a crucial role in allowing Benito Mussolini to come to power in October 1922. It is to be remembered that, unlike Hitler in Germany, Mussolini didn't become Prime Minister as a result of regular elections, but after a coup. The Fascists at the 1921 elections had won just 35 seats (out of 535) in the Chamber of Deputies and they were a minority party. Mussolini took advandage of the very complex social and political situation after WW1 and gained approval, but the "March on Rome" would have been very easily crushed by the army, if only Vittorio Emanuele had decided to do so. The Italian government at the time had prepared a decree declaring the state of siege, which was ready to be signed, on the King's desk. VEIII had told the Prime Minister Luigi Facta he would sign it, but he ultimately changed his mind, and appointed Mussolini Prime Minister instead. It's mainly VE's responsibility if Mussolini got to be Prime Minister in the first place. Some italians were already fascists back then, but definitely not the majority. Unfortunately, over the following years the vast majority of Italians would become fascists, and I am very well aware of it. In the first few years of Fascism, by the way, there were a couple of occasions where the King could have dismissed Mussolini while being backed by the majority of the population (I'm mainly thinking about the period of political crisis following Giacomo Matteotti's assassination in 1924), but he unfortunately failed to do so.
Of course, I understand that he was in a very difficult position and various factors might have influenced his choices, and I also think that up to that point Vittorio Emanuele had been a good monarch, who had a role in the victory in WW1, and who was fairly modern and liberal, despite coming to the throne in difficult circumstances after his father's assassination in 1900. Had he died in 1920, he would have been considered almost a national hero, the true heir of his namesake grandfather, "The Father of the Fatherland", Vittorio Emanuele II. Unfortunately for him, for his Royal House and for his Nation, history would judge him differently.
That said, I agree that the exile imposed to the male-line descendants of the last King of Italy was excessively harsh and way too long, and I hope that the relationship between the Italian Republic and the House of Savoy will improve (the Savoys were fundamental in the Italian unification in the 1860s), but I can't see them having any kind of semi-official role as it's the case in other countries.
