Good point, dad. I don't think there were any denunciations, just as there weren't any when St. Leo the Great claimed to speak with the voice of St. Peter in his famous Tome.
True enough...tempered by the fact, however, that St.Leo's Tome was not accepted from the get go (but only after serious examination and debate by the Council Fathers...even amongst those who approved of it, there were those who tought it sounded too "Nestorian-ish" and demanded clarification). Thus showing, as you indicate, that Rome's "primacy" was not at all like the aggrandized version of Roman primacy from later centuries.
"Ignatius, also called Theophorus, to the Church that has found mercy in the greatness of the Most High Father and in Jesus Christ, His only Son; to the Church beloved and enlightened after the love of Jesus Christ, our God, by the will of Him that has willed everything which is; to the Church also which holds the presidency in the place of the country of the Romans . . ." (St. Ignatius of Antioch, Letter to the Romans, Address).
This excerpt, whether you realized it or not, demonstrates one of the problems of latter Roman teaching on Church authority - their thought had ceased to be ecclessial.
For example, St.Ignatios' praise is directed not at the Bishop of Rome (who it is doubtful had "Pope" as an official title at that point, though perhap's it's beginings... much like Bishops/Priests were called "Abba" or something similar), but at the Church of Rome
. The prestige of Rome's Bishop, is a reflection of his Church's prestige/heritage.
This is in fact quite similar to St.Irenaeus' comments on Rome; they are a meditation not on the "papacy", but upon the universality/representative nature of the Church of Rome. Rome was the center of the known world at that time, the Imperial city, and a city consecrated with the blood of numerous martyrs (including Ss.Peter and Paul!). Indeed, just as martyrs came from throughout the world to Rome to meet their end, there is a real sense in which the faith of the world resided in Rome as well.
A similar situation is to be found in St.Clement's letter to the Corinthians. What few readers of this text keep in mind, is that St.Clement is writing in the name of the Roman Church, and not on his own. Indeed, it is not at all clear he was in fact the Bishop of Rome at the time when he penned the letter, rather than simply a presbyter. There are a few internal factors vindicating this view...
1) It speaks of the martyrdom of Ss.Peter and Paul as being something recent (which occured in aprox. 64 A.D. - not matching the period when St.Clement was in fact Rome's Bishop)
2) It speaks of the Jerusalem Temple and it's sacrifices as still being active - something not possible of the text was authored any later than 70 A.D. (when Jerusalem, and the Temple, were leveled by the Roman army due to the uprising of the Jewish zealots.)
3) The problems in Corinth (described in the letter) sound like they are in keeping with the antics they were pulling at the time St.Paul wrote his epistles to them. While not strong proof, it would seem more likely that the authoring of 1st Clement would be closer to the time of St.Paul's epistle, rather than several decades later.
While the exact status of St.Clement is significant, more significant is that he writes as one speaking for the Roman Church.
All of this however (Rome as a Church being what was important, not so much the pastor of the Roman Church) is overlooked by people reading these texts in the typical, anachronistic fashion (reading later Roman aggrandizing into the texts.)
It is certainly true that by the end of the fourth century, the Bishops of Rome were beginning to emphasize their own importance more and more (primary evidence being the letter of Pope Damasus). However, it's very hard to not notice the change that had occured in so doing this - by this point the emphasis is very much on the Pope as an individual (and not so much on the prestige of the Roman Church), and very intererstingly, an almost complete emphasis upon the "petrine" heritage of the Roman Church (with little mention at all of St.Paul, who most likely had as much to do with the Roman Church's formation as St.Peter did.)
Personally, the best explanation I have for this is that as the Church spent longer and longer as a "legit", "legal" entity, it began to theorize and give more consideration to the notion of the Church as a universal whole - it is in this climate that St.Cyprian's universal ecclessiology begins to be formed as well. It is also true, that when you have a large body together, somebody has to be "the first" and step up to exercise some leadership. I think it's in this climate that Rome developed
a theory of it's own authority amongst other Bishops, based upon an older, widely held respect for the Roman Church and Her heritage.
While this older respect was certainly held throughout the Christian world, it's quite obvious that Rome's opinion of herself (particularly as this appraisal grew with time) was not universally held onto, at least not with the same kind of tenacity. One need only compare the attitude of those Fathers who were within Rome's patriarchal juristiction with those who were not - a much different tone and level of emphasis.
In short, Rome's latter views of herself were more or less provincial in nature - they certainly were not oecumenical, but were a widely held to (in the west at least; though not without exception) model for Church polity.
I think where these views took a sharp turn for the worst, was when the political ambitions of the Franks got out of hand, the death blow being when Franks started actually sitting in the "Chair of St.Peter". It is at this point that the modern papacy as we now know it begins (since actual Roman Popes, like St.Gregory the Great, had a big problem with ideas like "universal juristiction", as his letter to St.John the Faster made clear).