I've been reading Book 4, chapter 7 of The Institutes of the Christian Religion, in which John Calvin offers a brief history of the Roman bishop's claim to sovereignty over the universal Church. Perhaps that has led me to reflect on Church history in general, and the Great Schism in particular.
With many more thoughtful Roman Catholics, I regret that one effect of the Protestant Reformation was a division of the visible Church into various distinct, and often competing, branches. However, I cannot agree with the solution to that division proposed by many of the same Roman Catholics (particularly those with the zeal of recent conversion to the cause): namely, reunification with the Roman Catholic Church. These tend to paint division as a protestant disease, one which can easily be cured by submission to the pontiff in Rome.

In other words, protestant division is not alien to Roman Catholicism, but intrinsic to the post-1054 character of Rome (and Eastern Orthodoxy, for that matter). Peculiarly, Roman Catholicism continues to recommend as a cure for division precisely that which led to the Great Schism: universal submission to the papacy. For Protestantism, this is anathema, while for Eastern Orthodoxy it is primarily distasteful. Why, then, does Rome continue to insist on it? To this Protestant, it seems Rome would prefer division to surrendering its false claims of supremacy.
Schism is the great sinful legacy of the Protestant Reformation, and I agree with our Roman Catholic critics that Protestantism is unnecessarily divided against itself. But to the extent that is so, we are merely following a tradition inherited from our time sojourning in Rome after 1054. The root of Protestant division is in the Church's Roman Catholic history, and today's Roman bishop would have far more credibility when he makes ecumenical pronouncements if he were actively seeking to root it out.