Apostolic unity and church structure in the first century

I sometimes wonder just how unified the band of the apostles was in the first century. The answer to this question might provide some insight into the way they implicitly or explicitly understood the Church to function.

My hypothesis is that the apostles generally considered themselves to work independently of one another, each having the right to preach the Gospel and found and care for churches without the intervention or management of the others. This implies a conception of the Church according to which its principle of unity is not its submission to a single, well-defined hierarchical structure but rather a shared faith in Jesus more fundamental than its plurality of manifestations and idiosyncrasies. It was the message of the Gospel that made the Church to be one and not a well-structured institutional body.

There is some evidence for this hypothesis, I think.

• The apostle Paul mentions that he typically goes around preaching the Gospel in places where there are not already churches “so that I do not build on someone else’s foundation” (Rom. 15:20). He treated other preachers as independent of him and as having the right not to be interfered with, a right he presumably also claimed for himself.
• Paul elsewhere says of Peter, James, and John that it “makes no difference to him” whether they are or are not acknowledged leaders of the church in Jerusalem, because “God shows no partiality” (Gal. 2:6). His concern is to have the freedom to preach the Gospel of Christ and not in the first place to submit to some purported overseeing ecclesial hierarchy.
• The fact that there is no mention whatsoever of the majority of Jesus’s disciples and twelve apostles in the New Testament after the ascension, indeed that there is not more mention of the various apostles by name in the New Testament documents that have survived, strongly suggests that these persons all went their own ways and did their own thing after a point in time, no longer keeping close communication with the others.
• The entire “Quartodeciman controversy” is evidence that the apostles left different traditions to the churches they founded, suggesting that they did not regularly consult with one another or pass down a perfectly uniform message in every detail. John in Asia Minor left a different tradition about the celebration of Easter than the other churches in other places of the Empire had received. This piece of evidence is especially noteworthy because John’s churches in Ephesus were not particularly far removed from other apostolic centers, like Corinth, Antioch, and so on.

I will be returning to this issue in the future as I continue to do my research. But here are some initial lines of evidence in favor of my hypothesis.