I was going to sleep on it, but I doubt my answer would differ much tomorrow, so here are some shots from the hip...
- It seems clear that Rome held a place of primacy in the pre-schism Church.
- It appears that Rome even held a place of “presidency” (i.e., “presiding in love.”)
- Rome appeared to be the sounding board for orthodoxy.
- The East and West had political issues with each other and even minor liturgical issues, but the separation was not a question of orthodoxy.
- The Orthodox Church seemed to stop looking towards Rome as a sounding board for orthodoxy not because it was un-orthodox, but because of political issues.
- If Rome presided in love, held the presidency, and was used as the litmus test for orthodoxy, why would the Eastern churches abandon it due to political issues.
I have not seriously thought about these issues in depth since 2001, when I was trying to discern whether I should be Catholic or Orthodox. I sided with Orthodox at the time, and was received into the Orthodox Church. I don't think I was mistaken in that choice. However, I felt pulled both directions at the time (even at times when I was an Orthodox catechumen), and I must admit that if I had to make the choice right now I'd still feel torn. The issue just isn't as clear cut as the apologists on either side make it out to be, IMO. Nonetheless, like I said, I don't think I was wrong in the choice I made, and I still agree with the Orthodox arguments more than the Catholic ones when it comes to papal supremacy/infallibility, the schism, etc.
I would agree that Rome had a unique position in the early Church. I think it would be anachronistic to say that all the Churches saw Rome as their ecclesiastical head, having universal jurisdiction over the entire Church, but Rome certainly seemed to be considered the most important local Church. But the reason for this importance seemed to vary, depending on who you asked. For some, maybe it did have to do with Peter (and possibly Paul). For others, it was the generally consistent faithfulness that Rome had. The Fathers of the Fourth Ecumenical Council seemed to have something entirely different in mind, however:
"For the Fathers rightly granted privileges to the throne of old Rome, because it was the royal city. And the One Hundred and Fifty most religious Bishops, actuated by the same consideration, gave equal privileges to the most holy throne of New Rome, justly judging that the city which is honoured with the Sovereignty and the Senate, and enjoys equal privileges with the old imperial Rome, should in ecclesiastical matters also be magnified as she is, and rank next after her" (Canon 28)
And people generally did look to Rome for guidance, that is true. But this was not always the case, and as time passed and Constantinople matured, some responsibilities began to be transferred to the new imperial city. To again quote the Fourth Ecumenical Council:
"And if a clergyman have a complaint against his own or any other bishop, let it be decided by the synod of the province. And if a bishop or clergyman should have a difference with the metropolitan of the province, let him have recourse to the Exarch of the Diocese, or to the throne of the Imperial City of Constantinople, and there let it be tried." - (Canon 9)
And Rome was not without controversy or moral or doctrinal lapses. The most famous--and argued over--example is probably that of Pope Honorius. However, I have already read of other disputes. St. Cyprian of Carthage, for instance, seemed to praise Rome when it suited his needs, and then publically disagreed with Rome at a later time. Then there was St. Jerome. Whether the Council of Rome of 382 dealt with the biblical canon, as some have asserted, I don't know for sure. But whatever the case, it does appear that Jerome, in favoring the Hebrew canon over the Septuagint, disagreed with Pope Damasus and the Roman Church (this in spite of St. Jerome being the secretary of Pope Damasus). The point being, the early Christians were fine with giving Rome it's due whenever it served to promote orthodoxy, but they seemed to have no issues with disagreeing with Rome when they thought it proper, even when it came to important issues.
Regarding the fracturing of the Church... well, some of the reasons early on did seem like a bit of a stretch. In a letter from St. Photius to the Pope of Rome, which I read in an edition of the Mystagogy of the Holy Spirit that I used to have, St. Photius mentions some differences between the east and west at the time. The differences were rather superficial, like whether priests should have beards and such. And if I remember correctly there were a couple practical matters. But the filioque, so far as I can remember, was the only significant doctrinal issue brought up. Now, by that time (c. 9th century) papal supremacy was starting to become an issue, if I remember correctly, but perhaps it was not a deal breaker yet. Whether you consider the filioque a major doctrinal issue or not, I don't know, but apparently some eastern theologians did.
I guess that period is confusing. The Romans still consider an anti-Photian council Ecumenical, I think. And some Orthodox have responded by giving significant weight (or even full Ecumenical status) to a pro-Photian council. Yet in spite of that mess, the local churches still somehow came together and were in communion for a few generations after that. Of course we like to date the schism to 1054 for convenience, though Roman Pope's name struck from the diptychs in Constantinople a decade before that, and others would place the final and definitive split until the 13th century. Whatever the case, I do not think it is fair to say that it was all political. Surely politics and culture had a part to play. That crack had been growing larger for centuries. But it did go beyond that, IMO. By that time there really was a strong idea of papal supremacy in the air, and also some other issues that needed to be worked out like purgatory.
Rather than putting the focus on political issues, I would say that there were political, cultural, and doctrinal issues that were all developing at the same time. Maybe politics played a very public and prominent part. Well, that was true in the 4th and 5th centuries as well, when you read about this or that local Church interfering in the affairs of another local Church. From the time that Emperor Theodosius made Christianity the state religion--and perhaps even from the time Emperor Constantine issued the edict of toleration--politics played a significant, and sometimes unfortunate, part. And maybe when you had Persians and Muslims and "northern barbarians" to deal with, when there were arguments over the evangelization of this or that group of people, etc., politics got the lion's share of attention. But who would deny that papal supremacy was there from fairly early on, building as the centuries passed?
Anyway, that's my two cents. When I think of these issues, I think of the Ecumenical Councils. It didn't matter to easterners whether the Pope approved of what the East was doing at, say the 2nd or 4th Ecumenical Council. So far as I've read (despite some posts I've seen on this forum of late) it's my understanding that the presidents of the 2nd Ecumenical Council weren't even in communion with Rome at the time it took place. But the Easterners didn't say "Oh, we can't compose that canon, Rome would never approve!" or "Well we can't call a council yet, because Rome won't give it's ok to it". Rather, the eastern local Churches went about their business, doing the best they could, and if Rome wanted to wait a thousand years before they would recognize certain canons or whatever, well that wasn't any concern to the other local Churches. For a long time, Rome was generally like a wise big brother, but she was never an like a Father who had total control (ie. universal jurisdiction/supremacy).