When Italy unified, didn't they ponder the idea of making the pope head of state?
In 1870? No. Before the 1848 revolutions there was a movement that wanted to unify Italy under the pope but during the year of revolution Pius IX crapped that up. After that the papacy became the main enemy to unification. Either change Pius' mind or kill him off and you have a whole nother can of worms.
The Ultimate Papal Wank in real people speak: Hundreds and hundreds of dancing altar boys prancing around the Vatican as cherubs steal their robes
The Ultimate Papal Wank in AH people speak: A Borgia-like pope gets himself elected in time to be around when the Italian Unification movement heats up. He accepts their offer to be the symbolic leader of Italy but once unification is complete, decides to usurp power for himself. And he keeps it.
He pulls a series of five year plans out of his vestments and turns Italy into an industrial and military power.