The very real downside if you're Catholic is they may pay all their taxes to the pope and provide you zero troops for the entire duchy. This is true if they like the pope more than you. What a lot of people don't realize, however, is that they break ties in the pope's favor. So if they're at 100 with you, and 100 with the pope, they pay the pope. This happens a lot more than you think -- pretty much after every successful crusade they will be at 100 relations with the crusading pope. Which means you will see no taxes or levies from them until that pope dies, no matter what you do. If every vassal is a PAB, that can be very bad for you. It doesn't matter if you rule over all of Europe if not a single vassal will send you cash or levies.