Well, if "taking turns" can include time ranges in years and decades. Although there is no term limit for pastors, Southern Baptists can elect them off, and still do so at a relatively high rate, and firing liberal-minded pastors in droves was indeed a key measure in the fundamentalist takeover of the church. Even if that weren't the case, I think it matters a lot that congregations choose their own new pastors, thereby giving the fundamentalism grass-roots continuity. Perhaps even more importantly, the attendants of the annual assembly (which sets dogma and has some control on the Executive Committee, which would complete the hierarchy you mentioned) are elected annually from the congregation. The fundamentalist takeover used elected bodies and positions to grab appointed positions and re-write rules and doctrine (rigging the game in the same way as it happened in the simultaneous conservative takeovers of the Republican Party, the media and the federal government).

_{*Lunatic*, n.
One whose delusions are out of fashion.}