In terms of the Catholic Church, I find exactly what I mentioned in the essay to be detestable. The idea of there being a level of purity which almost nobody else can replicate unless they are prepared to kill for an authority backed by strictly papal and religious doctrine. It's a level of purity which not only looks very sinister, it is impossible to completely achieve to the insane standards which require it. It is a form of self-destructive fascism in-which the warrior classes are being converted into anti-secular knights that fight unbelievers and other enemies of the church. One must be clear when discussing the vast differences between purification and compromise within societies: one of them is practices every day by almost every government, the other is probably being attempted by the North Koreans to a certain degree of success but at the cost of every citizen there (from birth) amounting to nothing but property of the state; all you need to do is think about other regimes that wish to adopt a level of 'pure' ideology onto their state's population in the past as well as the present: Chairman Mao's 'Cultural Revolution': the determination to reassert 'true' Communism in China; Stalin's great purges of the 1930s that attempted to 'cleanse' pretty much everybody that was deemed not fit for such purity of ideology; Hitler's Lebensborn system to adopt a pure ideology based on preserving a pure Aryan race whilst simultaneously exterminating other races. All of these are examples of a society which had attempted to adopt a policy of purity to some extent. The Catholic Church, although not completely successful in its attempt to create a pure society, can certainly be said to have attempted it through religious doctrine.
**As an aside, I read your essay and thoroughly enjoyed how well it is written.**
I think it is anachronistic presentism to assume that medieval secular forces were a viable option for foreign campaigns in the medieval period. Modern states did not exist and effectively every army was sworn to the service of a monarch. Placing mixed armies into foreign campaigns could only transplant conflicting parochial interests (and the individual opportunism of soldiers) into close proximity. Military orders, whose membership was voluntary, became an important aspect of multilateral coordination because religion was able to unite disparate loyalties/agendas, and - without domestic treason - eliminate feudal and personal opportunism from what were effectively remote humanitarian missions. I don't think that it can be argued that military orders were part of a larger agenda to transform secular armies, nor Christians at large into a theocratic empire, because military orders were never effectively stationed outside areas subject to foreign attack(mostly, but not exclusively islamist). By 1500 most of the military orders had been suppressed.
There is a distinction between contemplative and active orders in the Catholic Church - the contemplatives, as the name suggests, are places of intense spiritual/meditative focus, with strong associated activities of scholarship, art, music, etc. The active orders are directed towards particular needs/activities, which could not effectively be addressed by either national, nor personal interests. In the era of the crusades you would have various orders established for the ransom of captives. Religious in these orders would exchange themselves with lay/secular captives (what we would call hostages), until funds could be raised, by the order, to pay the islamists' ransom fee. When particular missions were finished/exhausted many of these orders would be suppressed.
In the present era we have had The League of Nations, NATO, The United Nations, The EU, and other iterations of international military cooperation. Back then such cooperation was coordinated by the Church. Whether it is legitimate for a Church to step into that role is arguable, but within the historical context, it was very necessary. I think it is a very large and ultimately false intuitive leap to claim that strict requirements imposed on soldiers, to attempt to form a more unambiguously humanitarian army, had a broader application, outside the actual function of that army.