Actually we can go backwards. When trouble erupted in the early churches when the apostles were still alive those churches appealed to the Chair of Peter and Rome for a resolution to local issues. An apostle was not sitting at the seat at that time.
Case and Point
itās generally accepted that 1 Clement was written about 96, and that the Apostle John died about 100. So what? Well, consider how 1 Clement begins. Pope Clement, speaking on behalf of the entire Roman Church, says:
The Church of God which sojourns at Rome, to the Church of God sojourning at Corinth, to those who are called and sanctified by the will of God, through our Lord Jesus Christ: Grace to you, and peace, from Almighty God through Jesus Christ, be multiplied.
Owing, dear brethren, to the sudden and successive calamitous events which have happened to ourselves, we feel that we have been somewhat tardy in turning our attention to the points respecting which you consulted us; and especially to that shameful and detestable sedition, utterly abhorrent to the elect of God, which a few rash and self-confident persons have kindled to such a pitch of frenzy, that your venerable and illustrious name, worthy to be universally loved, has suffered grievous injury.
What does this mean?
It means that when there was schism within the Corinthian church, they appealed all the way to Rome for assistance and consultation, even though the Apostle John was alive at the time. We donāt know exactly when the Corinthians wrote, but it was early enough that Clement is apologetic for his delayed response in 96 A.D.
Apart from the pope and the Apostles, no one is afforded this kind of respect and deference in the Apostolic age. And when Clement responds, heās not afraid to order the schismatics to return to the true Church:
Ye therefore, who laid the foundation of this sedition, submit yourselves to the presbyters, and receive correction so as to repent, bending the knees of your hearts. Learn to be subject, laying aside the proud and arrogant self-confidence of your tongue. For it is better for you that you should occupy a humble but honourable place in the flock of Christ, than that, being highly exalted, you should be cast out from the hope of His people.
So you have the Roman church intervening in a local church dispute, and issuing orders. Youāve got the Bishop of Rome speaking on behalf of the whole church of Rome. And youāve got all this going on while the Apostle John is still alive. A standard Protestant ecclesiology would suggest that this matter would have been handled entirely at the congregational level, or barring that, by appealing to the still-living Apostle.