The conversion to Manichaeism would weaken the Sassanid power in two distinct ways. Firstly, Manichaeism is a religion based ultimately not in the Iranian cultural zone, but in the Syriac speaking world of Syria and Mesopotamia. Mani himself was drawn from a Syriac speaking millennial Jewish sect residing in Babylonia and his first and most skillful language was Syriac. Mani was immersed in the Judaic-Christian religious milieu and of course to Gnosticism, which at its heart was divergent to the Iranian view of the universe.
Iranian views during the classical period, while often dualistic, understood the world as under the possession of the Great King and the Great Houses, the Iranian elite therefore were ideal rulers, in their material/physical bodies. The Gods of the Iranian peoples co-habited this realm with them and were their ancestors, providing the Great Kings the wisdom, power and legitimacy to not only rule Iran, but in theory to rule all of existence. The Iranian Great King received his mandate by way of divine lineage and the 'aura of kingship' similar to Germanic kings in Europe, wherein the Divine embodied by the 'sun' (Mithra), granted the king his legitimacy through a process of illumination or granting of an aura and this is called the 'divine mandate.' Imparting of a kingly aura was not only a statement of legitimacy, but also that within the Great King, Divine Power was invested and in his words was the divine being, fully and completely divine and the true mediator of all creation to the divine energy of the heavens and the unseen gods all around mankind.
Mani presented the universe differently. According to Mani, the universe was not subdivided into a divine good and divine evil, but rather a realm of light arrayed against a realm of dark, with the earth being the 'mixing' placed of these two realms, with the dark having gained a 'momentary victory.' Mani attempted to try to appeal to the Great King by way of attempting to frame the Great King as 'Master of Light' and as a savior of all humanity and this was an interesting ploy. However, the issue despite all the flattery and grandiosity, was that implicit in the claims of Mani was a rejection of the Iranian kingship model. Yes, the Iranian king could be the savior and Master of Light, but to be that in the way Mani wished, the Great King had to accept the view that the world had been filled with darkness and that the Gods of yore were demonic and hence his claimed ancestors were also.
While that is an issue, I do not believe it is insurmountable... for one, the Germanic peoples of Europe were willing to slowly phase out their traditional gods and many of their religious customs to Christendom. However, there is a key division here between these divergent perspectives. Firstly, the Sassanid Great King, while great in bravado and famed for his sacrality, was of less sacred nature frankly than Germanic kings and his position was beleaguered by the Great Houses. The Great Houses, all supposedly kings in their own right, constructed an alternate mythos of sacrality that excluded the Great King near completely. Portraying the Great Houses as the Lord of the Realm and conquerors who were children of Darius and the mythical Kavanid dynasty, the Great Houses claimed to be of divine birth and of primordial stock ruling the land as near divine beings. The Great Houses would simply have never accepted Manichaeism as their personal dogmas without significant force, one that the Sassanid kings were not willing to utilize or lacked the power to do so.
Finally, Zoroastrianism, while also somewhat divergent and against the agenda of the Great Houses and also against the Sassanid's own dogma in the first decades of rule, was the best religion to adopt for the purposes of the Sassanid Great Kings. Manichaeism as I mentioned was a religion on the fringes of Iranian life, a foreigner faith with bases of power in the areas that produced the least soldiers and often made up people who were of diverse religious background hard to unite. Zoroastrianism meanwhile, was a religion based around a collection of orthodox, educated and zealous priests all deriving from the area of Fars Province and were heavily connected to the Sassanid kings by lineage and ethnic compatibility. The Zoroastrian priesthood were centered in Iran and possessed powers in southern Iran that the Manichaens simply could not gain without the direct support of the King. Further, unlike Manichaeism, Zoroastrianism was a religion that held institutional powers and capabilities within the Iranic world and hence more defensible against the Great Houses.
Eventually, the Great King would use the Zoroastrian religion to impose a clerical order and bureaucratic system to counter the power of the Great Houses and it is possible that the preference of Zoroastrians to Manicahens came from this understanding.