There is ample authority. FWIW, scripture proves your assumption that local churchs without central authority won't be in conflict is wrong.
What I said was "many of these controversies would cease to exsist."
There will be conflict within local churches. The Bible also addresses how these controversies are to be handled.
Take the example of gay bishop in the Episcopal church. If a local church apponted this man as bishop it would not effect the other local churches. As it is now it becomes a problem for all Episcopal churches under that central authority.