I think there is definitely an “American” religious identity, and as has been pointed out is rooted in modernism amongst other currents. American bishops like Ireland in Minneapolis and others were champions for such a thing. He even stated once publicly that the reasons the Church was having difficulty was specifically because she was not embracing modernism fast enough.
I suppose the simple answer to the opening post of this thread is that there is no need for it. There are Eastern Catholic churches with patriarchal and major archepiscopal jurisdiction already here. These would in no way benefit from being coerced into an American hierarchy (and both clergy and people would likely revolt en masse).
Observations of our Ruthenian brethren in their recent experiments to become more “American” liturgically (admittedly moving away from the official Slavonic books promulgated by Rome, mandated liturgical abbreviations and use of inclusive language even to the point of modifying the Creed, musical adaptations suited for the American singer, etc.) are not helping in this regard, either.
Note from Moderator:**
I moved the thread Why no “American” Orthodox Patriarchy? to the Non-Catholic Religions forum because it was directed to Orthodox participants and about Orthodoxy. This post began a new topic on an American identity in Eastern Catholicism so I moved it and the responses to it back to Eastern Catholicism. -Catherine