I guess I run my churches much like the OP does. In my camapigns, religion is the domanin of mortals, a structure set up and governed by men to worship gods. Gods don't run churches. They have slightly more important things to tend to. This being the case, religion and religious institutions are subject to all the foibles of mortality (e.g., greed, hubris, etc). Now, that said. . .
There are prophets in my campaigns, men or women who actually do have a 'direct line' to their god or gods (something that churches in general do not have). These folks don't spend their time interpreting religious texts to fit their own agendas but, rather, get their orders from the gods themselves, personally. In point of fact, many prophets are decried as charletains by organized religions because of the divide between what a given god really wants and what the Church is convinced he/she wants.
That is an astute set of observations regarding both the religious and spiritual life and how they sometimes overlap and sometimes work at counter-purposes.
In the world we play (I run it and my characters actually play in it) we use real-world religions, sects, divisions, (Christianity, Islam, Zoroastrianism, a few left over pagan cults, Judaism, and so forth) and what might later be called denominations, etc. and so it is rather easy to incorporate historical events and religious disputes, debates, ideas, ideals into both the general game and the events/actions surrounding and taken by the player characters.
But there is always tension, as well as sometimes mutual admiration and cooperation, between churches, mosques, synagogues, bureaucratic hierarchy, religious officials and administrators on the one hand, and mystics, monks, hermits, holy men, prophets, Saints and others who wish to see both spiritual and religious life flower in an individualistic way, rather than a strictly organizational, official, and/or hierarchical manner.
And the characters, one of whom is a monk, another a cleric, a third a mystic, are often caught in the middle between service to God and man, service to church, service to master or superior, and service to state, and how those various forces often have to operate mutually to achieve common goals and often conflict or oppose one another in the pursuit of varied goals.
It is interesting to watch my players and their characters struggle to sometimes try and reach compromise, and sometimes begrudgingly to oppose emperor or commander or abbot or bishop or maybe even each other when a particularly difficult religious or spiritual problem presents itself.
Of course as DM I don't really take a stand between who I think is right in any given situation; Bishop or Saint, Emperor or Church, monk or cleric, mystic or priest. I leave that for them to figure out according to the circumstances and how events play out and generally I try to write adventures that are complex and realistic enough that everybody might be right to a degree and everybody might be wrong to a degree. Or that the wrong party might be honestly earnest in their error, or that the right party too strict and overbearing in their demands. Then let the players see if they can contribute to a workable solution for everybody. Or not.
Anyway I thought your general observation was insightful.
