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The pope is not the cause of Dogma.  He is the necessary but insufficient means by which Dogma is revealed.  Dogma is the revelation of God.

Let me try to re-frame this discussion in another way.  Let us all remember this obvious, but in our day and age, corrupted truth.  There are not, nor will there ever be, NEW catholic truths.  Christ revealed everything that we must believe to save our souls.  The Catholic Faith is unchanging, fixed, immovable.

I bring this up because oftentimes when the pope/dogma is discussed, people incorrectly imply that the pope is of some necessity when it comes to keeping the Faith.  Practically, he is not necessary to keep the faith or save your soul!  You can pick up a good catechism and learn ALL that you need to save your soul.  The pope is a blessing, in that his job is to DEFEND the truth, or CLARIFY dogma, or RE-TEACH that which has been infected with error.  It is a blessing, because many popes don't use this power, or they use it unwisely, so when a good pope fulfills his office, then the Church has good days.  If he fails to defend, clarify or teach the truth, the Church has not failed, she simply has a leader that is poor at his job.  But, in all these things, as the bible says "there's nothing new under the sun".  The pope does NOT have the power to CREATE any new truths, as many imply by their over-emphasis on his importance.

However, the pope is important for the governance of the temporal affairs of the Church.  Without a head, the organization would implode.  He is, of course, very important for the spiritual aspect as well, but history shows that God gives bad leaders as a punishment for sin, so we can't expect for a holy pope to guide us to heaven.  At the end of the day, WE have to KNOW our faith, live it and teach it to others.  We can't, and shouldn't, rely on a pope to get us to heaven.  This is spiritual immaturity and irresponsibility.  This is not how it works.

This is why, practically speaking, the question of who is/isn't the pope is pointless. Sedevacantists aren't disturbed by a vacant chair because they know they must hold onto the faith regardless and that God will fix the situation.  They say: "The pope has lost his office because he hasn't followed the Faith.  I must continue to follow the faith to save my soul."  

Non-sedevacantists have the same logic.  They see a bad pope and realize he's a danger and that eventually, God will fix the situation.  They say: "The pope is to be ignored because he hasn't followed the Faith.  I must continue to follow the faith to save my soul."

The outcome is the same - follow the Faith, to save your soul.  I don't see the point in fighting over inconsequential details.

The problem is this is directly condemned by Pope Pius IX as being opposed to the Dogma “of the full power given from God by Christ our Lord Himself to the Roman Pontiff of feeding, ruling and guiding the Universal Church.” The “bad pope” people deny that the Pope has the authority to rule the rest of the Church in all things, not just when they use infallibility.

The pope's authority to rule the church pertains to his temporal power over the governance of the church and over spiritual matters (ONLY when he speaks infallibly).  The 'feeding, ruling and guiding' which Pius IX speaks of, is directly related to the use of his infallibility.  Again, the pope's job is to re-teach, re-clarify, re-proclaim that which has already been taught by Christ and the Apostles.  When the pope uses this power officially, he is using his infallibility.  If he uses it unofficially, he is teaching as a mere man, in which case he can teach good things and write good things if he is holy and trained properly, but ....he can also err either accidentally or for evil intents.