How did the RCC get so big? It's such a disaster. And from what I can tell, the longer it's separated from the East, the further it strays.
The rise of Islam, particularly among the Turkic tribes, eventually took from the EO most of their lands, with obviously Constantinople and the capitals of the Eastern provinces like Damascus and Alexandria being harbingers of their subjugation under the new Muslim order.
Constantinople in particular is an interesting (and tragic) case, in that its fall in 1453 was a part of the impetus for increased European exploration of the world, as the rise of the Ottoman Empire led to the closing of important sea and land routes to Europeans. Also the resurgent powers of Spain and Portugal, buoyed by their successes in the Reconquista, began spreading outward at this time, with people like Prince Henry the Navigator attempting to find a way around that would bypass the Muslim-controlled lands in Africa (at the time, they didn't know to what extent those lands stretched, and were working off of things like the "Prester John" legend; eventually the Portuguese would end up bothering the Ethiopians greatly, leading to the banning of the Jesuits from the country and the burning of their literature by Emperor Fasilides in the 17th century).
One can only wonder what might have been had Constantinople not fallen (another thing to 'thank' the Latins for helping along...), but the point is that when you look at the historical forces at work at the beginning of the "European Age of Exploration", you see a very weak and subjugated "Rum", and a rebounding and energized Rome. And so it was Rome and its affiliated kingdoms (the Portuguese and Spanish, mainly...at least in the beginning; the Dutch, English, and other by-then Protestant nations, as well as the French, would get into the act a little bit later) that colonized much of the world.
Who knows, maybe if the Eastern Roman Empire had held together and gotten into the habit of
conquest rather than making these kind of 'satellite' cities (e.g., Alexandria), you'd have people today in Mexico and Guatemala and other at least nominally Catholic places -- probably still speaking Mayan and other indigenous languages rather than Spanish, but maybe learning Greek as a language of classical education and status (no different than it was in Egypt or Syria among the ethnic Egyptians and Syrians in earlier centuries) -- worshiping natively as EO people, with no one thinking anything of it.
It's interesting to imagine where Roman Catholicism might be in terms of being a global religion if it had been as restricted in its ability to preach to the outside world as the Christian churches in the Islam-dominated lands have been (and still are, in many cases). I imagine it would still have a hold on places like Malta, Italy, and Poland, due to the cultural identification of people from that background with it (regardless of whether or not they practice it), but sub-Saharan Africa, Asia, and so on? The only parts of Africa to which the Roman Church had ever come not with colonizers were the Latin-speaking churches in North Africa (in today's Algeria and Tunisia, and arguably in
Mauretania, which extended into Morocco; not to be confused with Mauritania), which were wiped out by Islam. What other business does Rome have anywhere outside of Europe? They're not the first church of Africa, thank you very much, and as the bishop of Alexandria's role in evangelizing Africa shows (e.g., HH St. Athanasius the Apostolic sending bishops to the Nubian territories like Philae), many of the people Rome would later try to court would've been Christian at some point in their past -- just not of a kind that has any use for Roman Catholicism (whether we're talking about the EO or OO kingdoms in Christian Nubia, since that land had both. while the Latins themselves were something else; there was an analysis of the languages used in Christian epitaphs in Nubia done some years ago by a Polish researcher that showed several hundred in Greek or Coptic -- and many which were a mix of the two -- to something in the single digits to teens in Latin; if I recall correctly, it's in the Nubian Studies journal
Dotawo, though I cannot remember the issue).
The same point could be made far away from the Muslim lands, such as in India, where the Portuguese were apparently
so terrible in their treatment/'oversight' of the native Christians that it led to things like Nestorians breaking with that church to join the Syriac Orthodox in 1665, which was part of the fallout of the Coonan Cross Oath of 1653, where the native Christians gathered to reinforce their defiance of Latin dominance and denounce those among them who had cooperated with the Latinization/RC-ization of their churches by the Portuguese.
I'm not going to say that wherever Rome goes it messes things up and makes everything worse for people (there was a time, lest we forget, when Rome was fully and completely Orthodox according to both your guys' metric and mine, and that time lasted for several centuries), but I am going to heavily suggest that their history shows this to be the case both in the past in situations like these (accelerating the fall of the Eastern Roman Empire, royally ticking off the Christians of an entire subcontinent who had been there since c. 52 AD, when Rome had jurisdiction over jack squat, etc.), and now in the current crises when for whatever reason they
just can't stop enabling the rape of thousands of children. Lord have mercy. I don't get it at all, but it is indeed a disaster.
). 
