To be fair, the pope started those wars to stop Christian-on-Christian violence, and he was at least to some degree successful.
But yeah, the popular image of the pope ruling over Europe as an iron-fisted god-emperor whose every breath was taken as divine decree is...fanciful, at best; the pope had little temporal authority and was in conflict with secular leaders for pretty much the entirety of the Middle Ages.
I can think of a good number of cathedrals and churches higher on my wishlist than St. Peter's Basilica, but I would have no problem with it granting DV points or envoys (the latter synergizing nicely with the Vatican City city-state).