All of these are excellent points and I was going to go into it in my earlier post but I got too lazy to do it, so I'm glad that you did. What I would add is that in all religions there is a tension between "true believers" who think that a religion should avoid hierarchies and stay out of public life, versus the "help the people" group that thinks that a religion *has* to be out in the world where the people are.
The problem with the "true believers" approach is that hiding up in a monastery and saying prayers 20 hours a day doesn't seem to do much to help actual people in real suffering, and to a lot of religious people, that is important. Further, its insularity can lead to total inflexibility and stagnation, or even just irrelevance to the outside world. OTOH, the problem with the "help the people" group is that the more a religion has contact with the outside world, there are more temptations and that will lead to more corruption.
The Catholic Church has tended towards the more worldly, "help the people" view, and the Jesuits even more so (of which the current Pope is a member of). But as a result, it has often gotten involved in real world power struggles and fallen to the corruption that a more "pure" religion is less susceptible to. However, it also has a strong component of "true believers," with an option to lead a monastic life, while even clergy that deal directly with the public live a life that is very different from the public that they interact with (vows of poverty, chastity, etc). That flexibility to do both has probably been a big part of why the Catholic Church has lasted as long as it has.