I would argue one of the reasons is that the Sassanian Empire was founded by the ruling family. It was a dynastical polity. One of the elements of legitimacy was descent bound up in the trappings of divine favor. This can be seen from the inscription of Shapur I at Naqsh-e Rostam:

"I, the Mazda worshipping lord Shapur, king of kings of Iran and non-Iran, whose lineage is from the Gods, son of the Mazda worshipping divinity Ardashir, king of kings of Iran, whose lineage is from the Gods, grandson of king Papak, am ruler of Iranshahr"

Of course, such inscriptions are an example of royal propaganda, and should not be taken at face value. A ruler needs to take practical steps to ensure power is retained by themselves and their heirs to prevent usurpation, such as maintaining military authority or hegemony. Nonetheless, in ideological and administrative terms, the state was connected to, and reliant upon, a family in a way that was not possible in Rome.

Source https://faculty.uml.edu//ethan_spanier/Teaching/documents/ResGestaeShapurINAQSH.pdf