When people look at what draws them to Catholicism, you frequently hear about the sacraments, our liturgy, the lives of the saints, etc. When people want to grow deeper in their faith, they go to the Scriptures, the latest papal document, the latest lay grifter group making money off of slick branding of the Gospel (oh we'll get to you guys eventually), etc. Outside of the last option, these are all pretty good things to do.
I'm in a bit of a different boat. I deepened my faith by reading about the truly awful popes the Catholic Church has had in the past, and I loved reading about the abysmal state of Israel and Judah in the Old Testament. This wasn't something I came to as a traditionalist. Even upon first entering the Church I always took solace in God's mild rebuke to Jeremiah that if he cannot endure a race against men, how will he endure a race against horses? In other words, if you can't handle this now, what are you gonna do when things get really bad? A lot of people have had to answer that question over the years, and I find it instructive for us today.
Make no mistake, we have to answer that question. It is bad now, and it is likely to get worse. Our leadership is bad now, and its likely to get worse. How could it get worse than Francis, the dear traditionalist asks? This is where I think the studying of bad popes is instructive.
Unfortunately, many do this in a dishonest attempt to say "things aren't that bad today" because "hey, at least our pope isn't a moral scoundrel like in previous eras." Yet in their mistake, they do have a certain point that we should admit. Doctrinal errors and controversies are bad, yet their impact on history is not as great as believed.
Honorius was condemned by an ecumenical council for ambiguous wording surrounding the Monothelite heresy. Yet the impact long-term was negligible, outside of a few bits of Catholic trivia. Vigilius more or less created a schism over ambiguity regarding the Three Chapters controversy (or rather his mismanagement of it), yet the doctrinal error did not survive his deposition, as his successor abandoned his position, and within 50 years Gregory the Great did the first great retcon of Church history, who responded (more or less!) to questions about how Vigilius managed The Three Chapters schism with "Who?"
This might be cold comfort to the struggling Catholic of today who is troubled by Francis' remarks on a variety of things. Yet it is something we can take solace in: the pope's ability to influence history for a long time is limited, especially when on ambiguity in doctrine. We see this play out today. Remember the pope chastising the mother of a big family for "tempting God?" No? Well after making the remark, the Pope spent his next 5 or 6 general audiences trying to unscrew his screwup. Or his remark that most marriages today were likely invalid, and hence fraudulent? Not only has he never returned to it, any mention of the validity of marriages in that speech was memory-holed by the Vatican. Remember his musing about how assorted Catholics today were actually Pelegian heretics? The CDF released a document telling you to take the Pope seriously, but not literally. ("Clearly [CLEARLY!], the comparison with the Pelagian and Gnostic heresies intends only to recall general common features") The other ambiguities will work itself out in time. Yes, ones faith will be tried, but we have ample historical precedent on this one.
Another reason to study these unfortunate incidents in history is, in their own way, they reveal God's design, and point to the way forward. Here I speak of those moral scoundrels. And yes, we must be honest, there have been moral scoundrels. Anyone who says that every pope, by nature of being a pope, is clearly a saint (as you will see hagiography throughout history, and in practice in today's modern personality cult) has clearly never studied Pope John XII or Pope Benedict IX. Though somewhat rare, there were entire ages in the Church where the popes were less than exemplary, and the moral failings produced real scandals. (We should appreciate this more, but I'm already running long.) What we see is that it is the laity were the ones who drove reform. Sometimes it was a King or Emperor marching on Rome and helping to clean house. Other times saints were raised to launch reform movements. Sometimes the laity of Rome would just throw rotten cabbage at corrupt prelates that wouldn't reform. Sometimes all it took was one powerful lay individual to implement reform. Many of the reforms of Trent don't happen without powerful secular rulers or lay nobles working with Church synods. The era of feudalism and nobles might be gone, but we are not that different, and the laity can still be called to help ensure proper governance in the Church, and proper morals in her clerics.
I admit, the study of these dark times can be bleak, frustrating, maddening, and a host of other things. But there's also a glimmer of hope for our present age. It isn't just "In the end, we win." We do indeed win, but we win because God has given us a chance to fight that battle.