Yes, they go to mass, sing, pray for the Holy Spirits leading and I think that’s all marvelous.
However, the pope is a sinner just like everyone else and is not immune from the temptations that go along with an office of power and prestige. A little research into papal history will reveal there were some very dark popes along the way.
I’m sure Jesus prayed before choosing the apostles also.
You have the wrong idea about Papal Infalliablity but it’s common. I think you imagine Catholics believe the pope cannot sin. Others, think the pope relies on some sort of amulet or magical incantation when an infallible definition is due.
Given these common misapprehensions regarding the basic tenets of papal infallibility, it is necessary to explain exactly what infallibility is not. Infallibility is not the absence of sin. Nor is it a charism that belongs only to the pope. Indeed, infallibility also belongs to the body of bishops as a whole, when, in doctrinal unity with the pope, they solemnly teach a doctrine as true. We have this from Jesus himself, who promised the apostles and their successors the bishops, the magisterium of the Church: “He who hears you hears me” (Luke 10:16), and “Whatever you bind on earth shall be bound in heaven” (Matt. 18:18).
Some ask how popes can be infallible if some of them lived scandalously. This objection of course, illustrates the common confusion between infallibility and impeccability. There is no guarantee that popes won’t sin or give bad example. (The truly remarkable thing is the great degree of sanctity found in the papacy throughout history; the “bad popes” stand out precisely because they are so rare.)
An infallible pronouncement—whether made by the pope alone or by an ecumenical council—usually is made only when some doctrine has been called into question. Most doctrines have never been doubted by the large majority of Catholics.
Pick up a catechism and look at the great number of doctrines, most of which have never been formally defined. But many points have been defined, and not just by the pope alone. There are, in fact, many major topics on which it would be impossible for a pope to make an infallible definition without duplicating one or more infallible pronouncements from ecumenical councils or the ordinary magisterium (teaching authority) of the Church.