Carroll makes some often-overlooked observations. For example, he correctly relates the historical relation between the definition of papal infallibility and the loss of Rome's political power in the 19th century:
The pope was a supreme ruler only over the papal territories in Italy, and when he lost those in the humiliations of 1870, Catholic bishops rallied to him at the simultaneous Vatican Council I. His political collapse led to his spiritual elevation, with the bishops only then promulgating papal infallibility. Paradoxically, the pope’s claim to supreme Catholic authority, even over a council, rests on the council’s declaration.Of course, Carroll's comments will be (probably already have been) quickly dismissed without serious discussion by the most zealous of Rome's contemporary apologists. For them, the emphasis on Rome's distinctive element of the papacy is a positive, not a negative.
Nevertheless, Carroll's sentiments express the attitudes, more or less, of the conciliarists who opposed ultramontanism ("beyond the mountains" - a reference to the fact that the bishop of Rome is geographically distanced from many of the "Roman Catholic" churches). However, at least for now, the ultramontanists have won out. While Carroll views Vatican II as providing a measure of conciliarist reform, Carroll rightly notes that the current papacy (as well as the previous one, in which Ratzinger had influence) have sought to push ultramontanism to new heights while undoing any lessening of the papacy brought about by Vatican II.
Obviously, I don't endorse Carroll's opinions, but his comments raise the kinds of questions that Rome's apologists are uncomfortable addressing: the problems of the real historical development of the papacy.