Having been raised Baptist, but now being United Methodist, I’ve seen both the ‘independent local church’ concept and the ‘regional bishop’ concept at work.
There is nothing equivalent to a metropolitan in either system. Baptists certainly don’t have anything beyond the authority of the local church pastor as a guide for any individual church. Southern Baptists have the convention, but that really exerts no authority at all over local churches. Those churches are free to enter or leave the association at will and any number of times. It is basically a cooperative arrangement for missions and Christian education, but even that is entirely voluntary.
The Methodists are, I think, an effort to mirror the Anglican system, which they didn’t do a bad job of, except there is no equivalent to the Archbishop of Canterbury. In other words, there is no ‘bishop of bishops’.
Our bishops are over a geographic region (that we call a conference) much larger than a city, and their hold is important regarding placement of ministers in churches, but beyond that, the region is normally so many churches that they lose any ability truly to provide any kind of direction. Our ‘district superintendents’ might be a better parallel to a metropolitan in that they are generally centered on a major city in a smaller area within the bishops geographic region, but their authority is limited, dependent on a bishop to react to a district superintendent’s concerns.
Beyond that, we have no authority that seems to have the authority to enforce our doctrine and principles.
In that regard, I appreciate the Orthodox churches. They strike me as much more faithful.
The advantage of the Baptist churches, of course, is that the people definitely are the enforcers of their beliefs, and a pastor can be out on his ear if he goes astray from the doctrine of the people. For the most part, this is a good thing if there is a knowledgeable people. That isn’t always the case, though.
There's a lot of charm to that arrangement. Many advantage come readily to mind, long before contemplation of the likes of Rowan Williams.
After more discussion you had included the following charitable remark;
Even the "patriarchs" are (theoretically, anyway) not beyond some degree of correction in that system, I take it.
A guy (a bishop, metropolitan, even an archbishop) can (could?) always just apologize, and admit to being in error on some point or another, and if that not be as for change of doctrine -- which statements they naturally enough leave well enough alone, for the most part, then not need be embarrassed beyond recovery and continuance in the position.
It does take that, and a plurality of deacons who have enough education to support one another and whomever is called as pastor.
That's the down-side. The ill-effects could be (possibly) direct and immediate.
Cutting out the middle-men, so to speak, does leave the people of the church holding the bag -- right away.
I must confess though, that I'm not 'Southern Baptist', and was speaking to the best of my own knowledge about the way they go about things. I hope that I have not misrepresented any facts that I presented as such, while also venturing some amount of opinion not intended to be taken as well established, objective fact.