What is the overall purpose of leadership in the body of Christ? We could say that the basic purpose of all leadership is that all things may be "unto edification" (I Corinthians 14:26). Whatever the activity may be--praise, worship, teaching, spiritual gifts, fellowship, service to others, and so on--God's goal is that He would be glorified and every member built up in their relationship with Him. Nobody (including God) is interested in us just going through ritual or activity out of habit or duty with no edification. That has no meaning in God's purpose and becomes tiring very quickly. If something is not edifying (building us up in our relationship with God), it must be corrected. Will God correct things without using men? I have not found that to be true. My observation (in scripture and in experience) is that God corrects a situation and gives guidance through men that are hearing Him and willing to be used.
As I mentioned earlier, it may be possible for a small group to exist with minimal leadership, but even in that case I think we will always find some leadership. Somebody opens their home and states the time that fellowship will begin. That is leadership. Someone says they are not feeling well and asks for prayer. In response, someone leads in prayer. That is leadership. Somebody says, "Let's stop for lunch and continue our fellowship afterward." That is leadership. It may be minimal leadership, but it is still the leadership that is needed to help a gathering of people move together in an orderly way. By responding to direction through a member, we recognize the leadership which allows for an orderly gathering unto edification.
As a gathering grows in size, such recognized leadership becomes increasingly important. With just two or three families meeting together, the leadership requirements are minimal and easily carried out (even in a natural way). However, with 20 or 30 families, it is not so easy. I don't think that any of us are interested in only natural leadership. We want God, and thus we want spiritual leadership as we are gathering unto the Lord. In an open meeting where each member is charged with moving under the authority of Christ, how do we make sure all things are unto edification? How can unspiritual movement be corrected without hurting anybody? We want to hear God through every member. How can this happen? These are the challenges of leadership.
Some have solved these potential problems by organizing a program in advance, so that everything happens according to a preplanned schedule. But this has the effect of limiting the movement of the Holy Spirit and the spontaneity of every member responding to God. While some may be satisfied with such an "orderly" gathering, many of us who have tasted of something else are not content with that solution. We see the value of leaving a gathering open for each member to function under the authority of Christ. At the same time, an open meeting always leaves the possibility of members moving in their own ability and ideas and not under the authority of God. Having a recognized spiritual leadership is essential to be able to correct any difficult situations with wisdom and leave every member at peace and ready to move forward.
Another reason for recognized leadership is the need for private counseling. A member may be facing a problem which they do not want to reveal openly. To whom should they go? We may say they can go to anybody they want to, and that is true. But can immature or unspiritual members provide proper counsel? A member may decide to go to someone "their own age," or choose somebody they think will agree with them. But that may not be the best choice. It may become a case of "the blind leading the blind" and we know where that ends. Unspiritual members often need to be told who the spiritual leaders are, so that they can go to the right person. That means we need recognized spiritual leadership.
In general, elders facilitate the whole body functioning under the authority of the Lord. They do not "rule" in such a way as to push others aside or dominate. Rather, they give enough guidance to keep things orderly so that every member can function under the leading of the Holy Spirit and in the grace that they have. We may think this should all take place without leadership, but I think a good scriptural example would be the situation at Corinth. There were many things that were hindering the functioning of the body, but they were not dealt with until Paul gave some leadership. The leadership should have come from elders, but as they are not mentioned, it is likely that they either did not have elders or that they were not functioning properly. As Paul gave the needed leadership, the body was able to see more clearly and to take action together. The conditions that hindered were corrected and the testimony strengthened for the glory of God.