I think that's the biggest difference right there; Rome, somehow, managed to maintain central military control where pretty much everyone decentralized (or never got centralized; the Sassanids seem to have suffered fewer disastrous inheritance wars but were also apparently less centralized).
So the Duke of Somewhere could absolutely acquire power, but he'd be satisfied to play big-duke while ignoring the Crown and did not have to gamble everything on a mad dash to Paris/London/insert-relevant-overlord.
Mind, eventually this very principle also gave a pile of added legitimacy to the inheritance since it went undisputed a lot (such that the Dukes of Burgundy, even when they controlled Paris, shied away from trying to impose themselves as Kings at the cost of the legitimate Valois heir or the legitimate Plantagenet heir), making most crises occur when there was an inheritance dispute due to vague laws/priority.
This also explains places like Hohenzollern Brandenburg - they were not so much uniquely stable in principle, they just had piles of easy father-son inheritances (none other between 1471 and 1786, if I read wiki right).
I think the French and Sassanians are a good comparison because they are just so similar in many ways, from absurdly strong nobles dominating and enforcing cultural control and elite cavalry, to geographic constraints and susceptibility to "radical" ideology toppling both.
Rome actually did take the approach that other "blobs" like the Franks or Achamaenids did when faced with similar problems: divide the empire into semi autonomous regions only nominally under central rule. There we get differences: Iranians held onto very tight legitimacy rules and bled the periphery, Rome abandoned them and civil warred to unify, Franks ended up becoming contiguous but seperate states.
I guess at the end of the day I see three options (before modern technology):
1. Maintain central authority and hope to deal with warlords and power struggles. (Rome, China, and much much smaller states)
2. Delegate heavily and keep legitimacy/stability of the monarch at the cost of considerably less central power. (Ottomans, Polish commonwealth, most successful blobs really)
3. Fail to survive a succession intact. (Mongols, Macedonians, many short lived blurbs of history fall here)
Really a lot of the success of modern nations and the dominance of the powers that came out on top today can be seen as the outcome of efforts to centralize by combining both stable government with dominant central authority. Nations that pulled it off would go on to literally rule the rest of the world, those who failed to stabilize (Qing), or failed to centralize (Ottomans, Austrians, Indian powers, etc) fell behind. Until modern times though? Rome/Byzantines are normal.