I don’t know how much leeway even PP Benedict XVI has on the matter: while the actual title “Patriarch” (and thus its derivative “Patriarchate”) came into use only with Justinian and the Quinisext Countil (aka Council in Trullo), it was the Council of Nicea that first acknowledged the jurisdiction of the 3 Petrine Sees. The First Council of Constantinople went a bit further and acknowledged also Constantinople (“New Rome”) and Jerusalem, thus giving us the Pentarchy.
The title of “Patriarch” as used in several Sees of the Latin Church (I’m not sure if any survive beyond Venice and Lisbon) is strictly honorary.
To go beyond that would seem to amount to a Western version of autocephaly, and I highly doubt such a thing would ever be considered. The concept causes enough trouble in the Byzantine East that one would not expect it to be brought into the West. Further, the concept does not even exist in the Orient.
What perhaps
could happen, though, is the re-invigoration of the concept of “Primatial Sees” but even that would be rather meaningless without a return to the ancient custom of bishops actually
electing a Primate from among their number and having the election ratified by Rome, rather than having the Primate appointed by directly by Rome as is currently the case.
As alluded to above, the bishops of the 5 Sees (the Pentarchy) are Patriarchs
ex-officio. I do not see that a person other than the actual Bishop of Rome could be named (or even elected) “Patriarch of the West” without the act itself being in direct violation of the early Councils.
Any “new paradigm” would, of course, have to address the issue of “Petrine Primacy” which is a somewhat thorny subject. It’s also totally off-topic for this thread (and even this particular forum as a whole) so I won’t go there.