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It seems to me the spectre of the Roman republican ideal after the ascension of the Principate of Octavian caused many problems politically in so far as determining proper transfers of power after either the Principe or Emperor died.
Especially since the might makes right precedent established by Caesar made it perpetually difficult for any ruler, whether chosen successor or outright usper, to maintain legitimacy in face of the constant waxing and waning power of the Imperial court.
Therefore, if we take a potential PoD of say Octavian declaring himself King Augustus instead of "First Citizen" (consequences be damned) after wrapping up his war with Mark Anthony, converting the Senate into a kingly-court of advisors and instituting some semblance of kingly-succession rights..(a Roman version of Primogenture?)
Would such an arrangement have been better off for the spralling empire in the long run?