Few theologians shaped Anglo-Catholicism in the twentieth century more than Dom Gregory Dix. In 1938 he published a scintillating succession of articles contextualising papal power. Near his conclusion came the following:
The language of the Vatican [I] decrees on the Roman Pontiff is admittedly formidable at a first reading. ..."A primacy of jurisdiction, ordinary, immediate and episcopal" in every diocese in Christendom ... It is so unlike the powers we Anglicans concede to a Primacy. But is it? [Dix next refers to the episode when the Bishop of Exeter refused to institute a clergyman, Mr Gorham, to a benefice and excommunicated latae sententiae anybody who should do so; the institution was done by a Commission from the Archbishop of Canterbury. He goes on:] That was an act of jurisdiction in another man's diocese. It was an act of "ordinary" jurisdiction, since the Archbishop had an indisputable right, in the circumstances, to do it. It was an act of "immediate" jurisdiction, since he did not act as the bishop's delegate but against his protests. It was an act of "episcopal" jurisdiction, since it conveyed cure of souls ... the whole Vatican definition of a primacy ... !
In our own time, when the Bishop of Chichester, Eric Kemp, refused to ordain or license women, these acts were performed within the Chichester Diocese by Commission from Archbishop Carey, thereby providing another example of Dix's point. Carey as a reincarnation of Blessed Pio nono ... there's a thought.
The gist of Dix's arguments is that the early popes indeed did not exercise jurisdiction over the whole Church, but this was a period when Bishops didn't exercise jurisdiction either ... because the whole concept of canonical jurisdiction only came later and so is anachronistic. The sort of authority which popes did exercise in the universal church was exactly the same sort of authority that bishops exercised in their local church. When Vatican I defined the Petrine Ministry, it did so in the juridical/canonical language of its own period; just as the first four Ecumenical Councils framed their Christology in the terms of the Greek metaphysics of their own time (although, as Dix puts it, the Gospel writers had not been Greek metaphysicians). Swallow episcopal jurisdiction, you can't avoid swallowing papal jurisdiction. Swallow the anachronisms of Nicea, you can't avoid swallowing those of Vatican I.
No catholic-minded Anglicans need have problems with "the Papacy". Unless they want to have problems ... as an ignorant alibi for a disunity which for some reason they desire to perpetuate.