Not to get too off topic (oops...already there), but that idea would make much more sense if the ECCs weren't churches of people who already left
Orthodoxy for Rome. That's the whole reason they exist...to not be Orthodox anymore. Granted, this many centuries or decades later they are primarily composed of people who were born into this arrangement (and Latins fleeing the banality and irreverence of Rome while apparently still desiring to operate within the structure that made that irreverence standard for the largest of the churches in the communion, but that's another story). But it's not as if Rome can stop individuals from any rite from returning to Orthodoxy. It seems that for some it's more of a question of "where would we go if not here?" (And I don't mean that as an allusion to John 6:68; a Maronite acquaintance of mine recently told me that he should like to become Syriac Orthodox, as that is the most likely mother church of the Maronites if you do not accept Rome's contention that the Maronites "never broke communion with Rome", but that he feels it wouldn't fit quite right, as the Maronites are both Arabized and 'Europeanized' in a way that many Syriacs are not...so it's more like "this doesn't feel right, but it feels the least not-right of all options, because it's the one I know.")
Anyway, in an attempt to make this post relate to the OP more directly: It strikes me that both OO and EO already have an Orthodox Pope in the form of their respective Alexandrian Patriarchs, so I have to wonder if the recognition of an additional Orthodox Pope of Rome in some sort of 'special' role wouldn't in some sense be buying into Roman claims that were not universally accepted even back when we were all in union. I'm thinking here of Pope Leo I's letter to Pope Dioscoros of Alexandria, written some years before Chalcedon, which has been discussed here before (see this thread
), which is one of the several examples of requests from the Roman Pope of ancient times which were not heeded (poster "Witega" mentions several examples in post #7 of the linked thread). In the hypothetical world of a reunited Eastern-Western Church (I would include us OO in this, too, for the sake of argument), is it likely that the Roman Pope would accept being ignored, dismissed, or (heaven forbid) even deposed by those he had previously been understood to be "above" in some real, authority/governance-based sense? I think the answer to that question (which I think is a "no", and shows no signs of changing in my lifetime) says more about what Orthodoxy would or wouldn't do with a Roman Pope professing Orthodoxy. As I've often tried to tell my Eastern Catholic friends, the ability (or "privilege", in their case) to teach your own, non-Rome centered theology means nothing if you cannot also teach against
the errors of Rome on account of their incompatibility with your own theology. I would think the same would hold for the Roman Bishop in the reunited Church, when push comes to shove (i.e., he would have to be able to be deposed, as is in the Orthodox Church, not merely tender his resignation if he can be convinced to do so, as in the Latin Church).