If “the blues brothers” movie has taught me anything, it’s that Catholics and Protestants can find common moral planes to cooperate and resist tyranny.
Of course popes aren’t infallible on any level. But he must be the leader of the catholic faith without question, so he has to be right by definition. This was needed in the aftermath of the protestant reformation be cause the pope could no longer claim political leadership of the civilized world. It was to beef up his credentials when Rome lost political control so the catholic faithful would not question his authority as had become routine for developing democracies. Catholicism can’t survive as a democracy. So he needed to be perceived by the rank and file as not subject to their griping.
Think of it as the doctrine of “presidential infallibility” in place today by the Democrat faithful. It was a needed tool at the time.
Your analysis is revealing what helped you obtain your engineering degree.