Initially, as I noted earlier, the designation “Patriarch of the West” had a valid meaning simply because it was the one patriarchate on the Western side of the Roman Imperial “divide.” FWIW, IMO the designation “Patriarch of the West” is still valid since the evangelization and expansion beyond what was originally recognized as “the West” was accomplished from that very same West.
The other four Sees in the Pentarchy are named for their seat, and “Patriarch of Rome” could have been used from the start, but it wasn’t. To invent it now would really be atraditional. It would also likely cause some bad feelings since the “West” (i.e., the Latin Church) encompasses several separate territorial Rites (Ambrosian, Braga, Mozarabic, and Lyon). Albeit that all of them are rather small, all have legitimate traditions of their own, and while they are part of the Latin Church, they have never been part of the Roman Rite.
Anyway, if the title is to be replaced or revamped, it would seem to me that “Patriarch of the Latins” would fit the bill and probably be the most accurate rendering.