That theory still does violence to the indefectibility of the Church -- by effectively denying her essential mark of VISIBLILITY -- effectively placing the "true Church" in a hidden state. The SSPX, on the other hand, preserve the note of visibility, however, deny that the Apostolic See remains ever free from error. I don't know which is better off.
It would, by now, after 50 years (since 1958) of alleged sede vacante
on the Apostolic Throne of Saint Peter in Rome. With no legitimate popes.
But it is not impossible. But very implausible, I fear, as there would be little orthodox non-Vatican-II-accepting Catholic bishops of Latin or Eastern Rites left, who were appointed by Pope Pius XII and invested with ordinary
jurisdiction by the same ("last legitimate and valid") Pope.
There would be only a handful, and most who are left are fully supportive of the 2nd Vatican Council, as far as I know.
The SSPX does not claim the Apostolic See is not "free of error", but that the current claimants or occupants are in error as a private person
. If they claim the magisterium has taught heresy or error on Faith and morals, it would be heresy. But the 2nd Vatican Council has a lot from the authentic
magisterium and nothing from the extraordinary magisterium and quite some parts from the ordinary and universal magisterium. The statements that the celebration of the Eucharist by schismatic and excommunicated clergy of the Eastern heretical dissident churches "builds up the Church of God" is incorrect. But is it a heresy? An error in the practical realm perhaps, but error and heresy?
Anyway, the SSPX does not deny that the Apostolic See remains perpetually free of error
. It rather introduces a distinction between the person of the popes and their private allocutions etc., their mental state (allegedly not "capable" to grasp contradiction with "former" Roman Catholic defined teachings and holy Catholic dogma), and their official magisterium.
It is very complicated.
But it was not the SSPX who started the Crisis or the contradictions, or who now refuse to discuss and openly clarify all contentious points and alleged contradictions of dogma. It is the neo-modernist-influenced Vatican which refuses to do so. It were John Paul II and Benedict XVI who have continued to refuse to even discuss or clarify all contentious points, who veiled themselves in ambiguity and public acts contrary to the Faith (e.g. receiving a Messianic horn and kissing the Quran and inviting pagans to worship their idols for 'world peace'). Not the SSPX. Not Archbishop Lefebvre. There would have been no problems in 1957 under saintly Pope Pius XII. Or in 592 under Pope Saint Gregory the Great. No problems.
It is the Conciliar Church of Vatican II and its seeming contradictions, denials and ambiguity towards Catholic dogma and "previous" defined teachings of the Popes, which are the problem. The SSPX is merely an emergency ship.