Paul's Better Approach

It is my considered opinion that all of 1 Corinthians is about how to properly handle differences of opinion. As you point out, he castigates the Corinthians for how they handle them - by denominating. He says that that this practice is carnal and that he stands in doubt of them for it. As he says elsewhere:

Tit 3:10 A man that is an heretick [identified with a named group] after the first and second admonition reject;

In 1 Cor 13 he says that he will show a better approach (a "more excellent way") to handle differences of opinion, but to do say, he has to explain the principles that dictate his approach. These principles are the situation on the ground, the background, that makes his better approach the only wise approach.

A large part of his argument is that no one does or can know everything. We are all like children with a limited view. We all know a part. We can only see things from our viewpoint. Hence, we all need to listen. It is in the very nature of love, which is superior to all of the gifts.

The application then, in chapter 14, is NOT how "churches" operate. They operate 100% on the Corinthian model, not by the better approach. They emulate Rome, not Paul. The way that "churches" operate is by the pattern that the Catholic beast established, patterned after Roman government. You have a Poppa ("pastor") and a Senate (elder oligarchy), then you have the peons, who must conform to the dogmas that come from the top down.

Paul's "better approach" is ignored completely. It is considered archaic, outdated, impracticable, and dangerous. Here is what he said:

1 Cor 14:
26 ¶ How is it [the "better approach"] then, brethren? when ye come together, every one of you hath a psalm, hath a doctrine, hath a tongue, hath a revelation, hath an interpretation. Let all things be done unto edifying.
27 If any man speak in an unknown tongue, let it be by two, or at the most by three, and that by course; and let one interpret.
28 But if there be no interpreter, let him keep silence in the church; and let him speak to himself, and to God.
29 Let the prophets speak two or three, and let the other judge.
30 If any thing be revealed to another that sitteth by, let the first hold his peace.
31 For ye may all prophesy one by one, that all may learn, and all may be comforted.
32 And the spirits of the prophets are subject to the prophets.
33 For God is not the author of confusion, but of peace, as in all churches [gatherings] of the saints.

Verses 34 and 35 are likely later additions, based on textual evidence.

34 ¶ Let your women keep silence in the churches: for it is not permitted unto them to speak; but they are commanded to be under obedience, as also saith the law.
35 And if they will learn any thing, let them ask their husbands at home: for it is a shame for women to speak in the church.

Christianity as Paul described it is clearly extinct.