That's not really what this is talking about.They were to let the Spirit of peace arbitrate among them (Colossians 3:15) in the midst of ministering one another (Colossians 3:16).
Let the peace of Christ rule . . . in your heart. That's where this needs to happen, before matters even get outside the heart. This is about you having the right heart before God.
Once we've got a clear path from God in our hearts, THEN we will be able to minister to others, without it being just about whatever we think should happen.
All can and should be allowed to give utterance, teaching, psalm, prophecy, revelation, as the Spirit leads. Prophecy, dreams, visions, and the rest of spiritual gifts will be the hallmark of the end-time church.
All can . . . but not all should. We need discernment.
There are people in churches who want to be prophets but aren't. Who want to be teachers but aren't. And given the opportunity, will garner the attention to themselves, but won't be contributing from the Holy Spirit.
The overseers need to be strongly grounded in the Word, to be able to sort between these.
When I have 'the peace of Christ' for my idea, but someone else has 'the peace of Christ' for their idea, and its going to be this way, or that way, then there has to be a way to know the right way.
Peace subjectively in our heart has a better application in God leading us personally, it's just between me and Him. But in leading us as a group, and particularly when there is difference of opinion, we need to have a clear way to show everyone what is right, other than, "I just know God said I'm right and you're wrong! I have a real peace about that!" I'm sure you know the problems with that!
I believe that any church to be effective has to have a strong teaching ministry, not that other things are less important, but this is very important. Weak and inaccurate teaching leads to poor understanding of God, which fails to develop our faith, which leaves us less capable to walk by faith.
One last note: In congregations where the Spirit does not arbitrate among the members, this leaves the leaders - those most led by the Spirit and having the most spiritual authority - to intervene and keep the peace by force, i.e. through correction and rebuke if necessary. This is where you need strong, well-educated, Spirit-led and Spirit-empowered leadership, who will keep the Spirit on the throne of a congregation where He belongs, and not allow things to be given over to the enemy.
Hopefully not much force is needed! :)
But yes, there has to be someone to call the meeting to order sometimes. Ones who are known for their love for the brethren, so their correction is received in the right spirit. Ones who can faithfully and knowledgably apply the Scriptures, so the others can know this is God's way, and he's not just making it up.
I think the best way is to disciple your flock into a spiritual life, thinking heavenly things, getting into the habit of actively relying on God for everything, searching the Word to know Him better.
It's a tough one sometimes! To bring correction. To bring disappointment. And that people will receive it as a gift. So many don't.
Much love!