In all this you haven’t even mentioned the Caliphate, in its legal sense: the role it plays in “legitimatizing”, or at least legalizing, external Jihad.
As I understand it (according to a moderate amount of study), the Caliphate is essential to waging legal Jihad outside the borders of a Muslim polity. Per Immanuel Al-Manteeqi, for instance:
Only caliphs, for example, were granted the power to declare offensive jihad, because only they were taken to have the proper religious authority to do so (jihad being a religious “holy” war).
Al-Manteeqi’s note 18 references David Cook‘s’ Understanding Jihad.
(I haven’t read this (or similar) books, much less chased ref’s, which is why I describe my study as “moderate”.)
Al-Manteeqi goes on to quote Ibn Khaldun:
Ibn Khaldun (1332–1406), the most renowned Medieval Muslim historian, states the following in the prolegomena (Muqaddima) to his book on history:
Political laws consider only worldly interests. “They know the outward life of this world.” (On the other hand,) the intention the Lawgiver [i.e., Muḥammad] has concerning mankind is their welfare in the other world. Therefore, it is necessary, as required by the religious law [sharīʿa], to cause the mass to act in accordance with the religious laws in all their affairs touching both this world and the other world. The authority to do so was possessed by the representatives of the religious law, the prophets. (Later on, it was possessed) by those who took their place, the caliphs. This makes it clear what the caliphate means…
Having laid the framework for understanding the caliphate’s role, Ibn Khaldun goes on to note that,
(To exercise) the caliphate means to cause the masses to act as required by religious insight into their interests in the other world as well as in this world. (The worldly interests) have bearing upon (the interests in the other world), since according to the Lawgiver (Muḥammad), all worldly conditions are to be considered in their relation to their value for the otherworld. Thus, (the caliphate) in reality substitutes for the Lawgiver (Muḥammad), in as much as it serves, like him, to protect the religion and to exercise (political) leadership of the world.
(His notes 22&23 reference The Muqaddimah of Ibn Khaldun (warning: large PDF), parts of which I’ve read, although I was chasing other points at the time.)
The point of the Caliphate, then, is that it can make such atrocities as the 9/11 attacks legal: because the terrorists were acting under the aegis, and with the permission, of the Taliban “Caliphate” in Afghanistan, they were not criminals, they were soldiers fighting an asymmetric war.
(This also justified the US take-down of the Taliban “Caliphate”, which was responsible for the actions taken under its permission.)
Personally, I maintain an open mind regarding the legalities, under both Sharia and Western “Laws of Nations”, of the Caliphate. But the matter cannot be simply ignored in discussing ideologies of Islam and Jihad.