Gifts of the Spirit
Those who traveled between congregations had gifts of the Spirit. In the first century, folks with spiritual gifts were expected to share their gifts with other congregations. That included the apostles, prophets, evangelists, teachers, those with the gift of healing, those with other gifts.
Elders, on the other hand, were chosen to serve in just one single congregation.
Paul traveled between various congregations, and so did Peter, James, Titus, Timothy, Stephen and Philip. They had recognized gifts of the Spirit and they traveled among the congregations of the Churches of God and shared their gifts. With the exception of the apostles, they had no authority in the congregations they visited. They would teach, exhort and recommend, but they had no authority.
All first-century congregations were independent. No hierarchy told the elders and the other brethren what to do. There were no church pastors as we know them. Nor did they have to report to a headquarters organization. The Jerusalem church was not a headquarters organization; it was simply another congregation.
Antioch's unusual role
One of the most prominent congregations in the New Testament era was the church in Antioch. It had a unique relationship with the church in Jerusalem, and it was also the apostle Paul's home congregation. Much of what we know about the first-century church comes from the story of this one congregation.
It was also in Antioch that church elders are mentioned for the first time. The church in Antioch sent aid to the brethren in Judea by the hands of Barnabas and Saul (Acts 11:30).
The elders in Antioch did not travel to Jerusalem; Paul and Barnabas made the journey. Paul and Barnabas are nowhere called elders, but they are listed as teachers and prophets. The prophets and teachers, not the elders, traveled among the congregations.
Notice Acts 13:1-4: "Now in the church that was at Antioch there were certain prophets and teachers . . . As they ministered to the Lord and fasted, the Holy Spirit said, 'Now separate to Me Barnabas and Saul for the work to which I have called them.' Then, having fasted and prayed, and laid hands on them, they sent them away."
Paul and Barnabas traveled together and were directed by the Holy Spirit to raise up churches. They also appointed elders in every city to which they traveled (see Acts 14:21).
Once the elders were appointed, they were independent; Paul and Barnabas, even though they were apostles, had limited authority over them.
That is why Paul and Barnabas commended them to the Lord. The elders were to work together on local matters as they were guided by the Lord. They did not report to a hierarchy, nor were they controlled by a hierarchy, nor were they controlled by the Jerusalem church.
In the book of Acts we also have the example of Judas and Silas (Acts 15:22). Those two men were prophets from the Jerusalem church; they were not elders (verse 32): "Now Judas and Silas, themselves being prophets also, exhorted and strengthened the brethren with many words."
Again, it was the prophets and the teachers who traveled between congregations, not the elders. In this case Paul, Barnabas, Judas and Silas delivered a letter. They were prophets and teachers, not elders.
Why would the elders be confined to their congregations while prophets, teachers and others with gifts of the Holy Spirit would travel among the church at large?
It is because the unity in Christianity comes from the inspiration of the Holy Spirit, both on a local level and on the churchwide level. On a local level the elders helped maintain unity.
On the other hand, unity for the entire church came from traveling preachers and teachers. Unity did not come simply from elders exercising authority as a hierarchy allows them.
When congregations are independent, with no human chain of command over them, they are free to follow the Holy Spirit as it uniquely leads them. This independence of thought and action is true freedom in Christ.
A very real system of checks and balances is created. If a congregation goes astray, then the other congregations will see this. They will work to preserve the truth, and they will pressure the wayward congregation to return to the truth by their example.
When a hierarchy is created, mere men, usually elders, can force many congregations to conform to their ideas and an entire denomination can fall from the truth. That is the sad history of Christianity.
What the Lord instituted is better then what men have created.
Jesus set in motion a system whereby those who are chosen by men--i.e., the elders--should work in their own congregations.
And those with gifts of the Spirit should travel among the churches and teach as they are led by the Holy Spirit.
That is why all elders are local.