It (the infailibility of the pope) is also the reason of the great schism of 1054, when orthodoxy split from catholicism, officialy naming themselves ‘the orthodox catholic church’ (meaning basically the catholic church that has the right dogma; people mostly drop the ‘catholic’ from conversation nowadays though).
In the grand scheme of things, it didn’t do much good, eastern orthodoxy is just as corrupt and power-hungry as catholicism.