So why didn't Cardinal Mueller mention the Petrine Ministry in his Manifesto? I'm sure his attachment to the Decrees of Vatican I on the Primacy and Infallibilty of the Pope is as strong as my own.
(1) The question has been raised: does the question of the papal Magisterium concern the Christian Faith: or is it about the circumstances under which one might be told something about the Christian Faith? If the latter, then it may be that statements like "The pope is infallible" have a greater similarity to claims like "The Bible is true" than they do to such dogmatic teaching as the Hypostatic Union and Transsubstantiation or moral teachings such as the indissolubility of Marriage. And it would be very understandable for Cardinal Mueller to have left the papal function out of the equation at a time when the papal function is ... well, to put it bluntly ... not functioning. [To those might argue that some of what PF teaches is orthodox, I would reply that such a confused situation is more dangerous that a situation in which everything is untrue.]
(2) The Anglican dogmatic theologian Eric Mascall raised the question of how essential the Papacy is to the Church. I am sure that, as a permanent element in the Church's divine constitution, it is in one sense completely essential. It was placed within the Church to be, as an institution, the centre of Unity; of government; of teaching (most solemnly, when that teaching is ex cathedra). But is it essential in the sense that the Church ceases to exist during a papal Interregnum? Hardly. Mascall writes about an "extreme difficulty" produced "by the fact that, between the death or abdication of one pope and the acceptance of election by his successor, the Church is ... without an earthly head. ... it is a good thing for the Church to have a pope; it does not in the least show that it is necessary ... the pope is not of the esse but only of the bene esse of the Church. If he were of the Church's esse, we should have to hold that, during a papal vacancy, the Church simply ceased to exist. And this is no merely theoretical point; after the death of Clement IV in 1268 the papacy was vacant for two years, nine months, and two days."
I would add that, according to the Archbishops of Westminster, there was an interregnum of some seven years between the death of "Alexander V" [whom Westminster, rather oddly, claims to have been a true pope] and the election of Martin V in 1417.
But I rather doubt whether this is the sort of consideration Cardinal Mueller has in mind.
(3) I think a nimbler hare would be Blessed John Henry Newman's terminology about the Arian Crisis. He said that the Church's Teaching Authority was "in suspense" for about sixty years, during which time popes, bishops, and councils failed to Teach or failed to give orthodox teaching. (One of the English bishops tried to delate JHN to Rome for this analysis, but without success ... perhaps Pio Nono's business managers felt they enough hassle on their hands with Doellinger and Hefele ...)
I take Mueller's fine Manifesto as a sensible and valuable action to fill the gap at a time when PF has placed his Magisterium in Suspense by improperly employing his office to promote oddities, errors, and ambiguities which sound like heresies, instead of teaching the Faith which he received from his predecessors. The Manifesto looks like the nearest thing we shall get to reliable Magisterial teaching during this pontificate. It deserves to be used as such by those whose duty it is to set forth God's saving truth.
The Manifesto is an admirable and orthodox initiative to supply a need, and to forward the process of working towards the eventual restoration of what we have sadly lacked since the abdication of Benedict XVI: videlicet a teaching papacy.