Three points.As to the first point, there was indeed a Church in the British Isles prior to the coming of St Augustine to Canterbury. Father WB (the author of the comment above) wrongly states that it was "not established by Rome." It was in fact established by Roman Catholic Christians. This is evident by the fact that these Celtic/British Christians used only Latin for their Psalter, Mass, and other liturgies. It was a Latin Church that lost contact to the wider Roman Church on account of the collapse of the empire.
(1) What about the British Church BEFORE St. Augustine arrived at Canterbury? As you know, the sees of York and London (at least) date at least to the early 4th century and were not established by Rome.
(2) What if the pope is no longer "Patriarch of the West"? Are there not concomitant ecclesiological possibilities to do with the establishment of other patriarchates within the Western Church? Maybe this is unreasonable.
(3) But what about the establishment of an Anglican Use (or Rite) Personal Prelature, or again the establishment of an Anglican Use (or Rite) Personal Apostolic Administration, akin to that of Saint John Mary Vianney in Brazil?
There seems to be nothing endemic to Roman ecclesiology that would prevent one of the two possibilities of (3) above.
As for the second point, I believe it involves a very good question. I myself wonder if the Holy Father is considering something like "Continental Patriarchs," e.g. Patriarch of South America or Patriarch of Africa. This would certainly provide a stronger global structure. However, I don't think that the Holy Father's dropping the title Patriarch of the West is going to provide any future justification for Anglicans to have their own sui juris Church. It is just not happening.
As to number three, that is a very wonderful suggestion. But it is necessary for Anglicans to initiate something with Rome. Rome does not have the time or resources to create possible canonical structures and hope that people will come and fill them. Rome nearly always responds to a need (and usually very slowly). If you look at Opus Dei you see that it grew as a movement first and then later Rome provided the appropriate canonical structure of a Personal Prelature.
Thank you Father WB for the good comments and questions.