Because it is the only way to take away support from the Savoy cause, in Francis II case, ditto for the pope. I don't doubt that there will be other insurrections even without Garibaldi only less succesfull.
Actually, Ferdinand II of the Two Sicilies was the first to concede the Consitution. It was probably partially a move to spite the other monarchs, chiefly Pius IX and Charles Albert, but he did it nevertheless. The Pope as well conceded it, although IIRC he was the last one to do so.
Italy would not be ready for a war with Naples in 1870, if Francis II declares himself protector of the Pope, expecially because Papal States, even without Legazioni are bigger then Latium alone.