My experience in working with churches is that the vast majority of our governance models are controlling rather than empowering, permission-withholding rather than permission granting and deeply frustrating to leaders. As such, they prevent the church from being nearly as effective as it could and should be. In other words, our structure often compromises our missional effectiveness.
Structures do matter, because they either serve our mission or hinder our mission.
In a recent consultation, an executive pastor of a church of 500 told me a funny story. He needed to deal with some changes to a nursery ministry. When he asked around to find out who the nursery folks were accountable to, nobody really knew. He went to the elders (directional leadership) to explain the changes that he wanted to make, and then to the finance committee for funding, and finally to the 'general board' to explain again before he could accomplish the relatively minor changes he set out to accomplish.
Now if we really believe that the mission of the church is more important than the structure of the church, and that structures ought to serve mission, these kinds of tollbooths would be unacceptable. In such cases, the mission of the church has become subservient to the structure.
For some inexplicable reason (to me), church bylaws (and therefore our governance system) are often considered more sacred than Scripture! If you doubt that, think of some of the objections you face when you try to change them. Yet, many people do not realize that church governance is often driven by a combination of theological and sociological forces.
Consider the New Testament, for instance. Little is said about church leadership structures in the New Testament, apart from clear instructions for the senior leaders of a congregation called overseers or elders. While their responsibilities are clear, the structure of how they do governance is not.
In fact, the story of the early church is clearly a story of flexibility of structure as the needs of the church changed. Deacons, for instance, were added early on to deal with issues that the elders no longer had time to handle. As the church grew, senior leaders started to delegate major ministry issues to others. Today, many congregations have multiple committees or boards that are never mentioned in the New Testament.
My point is that there is nothing sacred per se about the structures that most churches have in place for leadership. Governance structures, apart from what is clearly spelled out in the New Testament as prescriptive, are simply tools that should be designed to empower people and facilitate ministry. Unfortunately many of our structures disempower and frustrate ministry.