Were the rules of the Abbasid, Umayyad, and Ottoman states based on the methodology of the Rightly Guided Caliphate, and what characterized the rule of these states?

The Abbasid, Umayyad, and Ottoman states generally remained on the path of Islam, but they did not adhere to the methodology of the Rightly Guided Caliphate. The Prophet, peace and blessings be upon him, described the political stages after him as beginning with a caliphate upon the prophetic methodology, then an oppressive kingship, then an tyrannical kingship, and then the return of a caliphate upon the prophetic methodology.