It's your conundrum...
"The pope cannot teach heresy, but if he does he is no longer pope. But the pope cannot preach heresy, but if he does, he is no longer pope - but popes cannot preach heresy! - but if he does he is no longer pope...."
Then you solved that conundrum using the mystery, the idea that popes are not popes because
cardinals were not cardinals, destroying the hierarchical structure of the Church in the process, it's just one of the casualties you needed.
Note that out of all the changes, the only thing the devil did not obliterate was the legal hierarchical structure of the Church. They must have known they could leave that up to certain laypeople.