It has nothing to do with restorations of monarchy. Forget about that. It has everything to do with the prestige and the dignity of a House, with respect for the patrimonium and the historical place of a family.
Families like Pallavicini, Odescalchi, Massimo, etc. have no hopes either to regain their once powerful positions but they do everything to preserve their prestige, their heritage. Vittorio Emanuele however gives the impression that he does not give any damn at all about this. Just jetsetting, partying, shopping, jetsetting, partying, shopping and his wife even beats him in that aspect.
His cousin Prince Aimone at least has done military service in the Navy, is doing real work (for Pirelli) ánd shows interest for the monarchist cause, for the dynasty and its patrimonium. Aimone simply comes over as a man with substance, with a goal in life vs that empty-head cousin of him with only interest in the next red carpet-event.