The very existence of religious Orders was a veiled rebuke to the perceived worldliness of the Church hierarchy. These monks with their vows of poverty, chastity and obedience were a positive example to increase the piety of the laity, whose faith and morals could easily be damaged by immoral clergy. Of course the Orders themselves could not openly say their way of life was right, and that of the higher clergy, with all its nepotism and simony and absenteeism, was wrong. But the striking contrast would have been plain for all to see.
And sometimes the Orders did come close to rebellion, like an order of Franciscans I read about that interpreted Scripture as saying that Christ and the apostles had no private property. The Pope had to nip this incipient communism in the bud, before it led to the notion that no one at all should have private property ( a logical assumption from the premise as Catholics are meant to follow Christ ). There was another group of extreme Franciscans called the Spirituals, some of whom were burned by the Pope, but I'm not sure if it's because they directly criticized the Church.
Most people automatically relate to the monks and see them as higher in the spiritual path. But the Popes, cardinals and bishops had to do the work of combating heresy, dealing with fractious kings and princes, the grunt work of keeping the Church together, looked down on by many as political, but absolutely necessary. I think an ascetical life is downright easy compared to the life of a Pope, with all the pressures and counter-pressures, not to mention the responsibility you would have not only in the eyes of men but of God. The papacies of Pius XII or Boniface VIII in particular, both of whom reigned during crisis points for the Church, must have been nightmarish. Much easier to be a monk living on bread and water, doing a little gardening from time to time!