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boag - Step back the truck there. The highest point of the Roman Empire when was everything was centralized. Meanwhile its experiments with decentralization was moments was when it was already declining. If it did helped, it doesn't looked that obvious. There's just too many factors in its decline to cite any single reason, but especially citing centralization when Rome was decentralizing during its decline.
The reality is centralization and decentralization are both rightful governmental approaches depending on the context. You don't want a distant central governments dictating every little matter and thing (Soviet Union for an example). You also don't want things to be decentralized into the hands of a few military strongmen (current struggles of Afghanistan, 1918 China). Or squabbling aristocratic fiefdoms (Holy Roman Empire).
Democracy isn't a third option either - it's tangential. You can have a centralized democracy or a decentralized democracy. While the act of voting is the most decentralized thing, one can be voting in a very centralized system (like voting in matters that it's execution perform by a very centralized seat) or very decentralized (like voting in a town hall). Also when question is about increasing stability, getting a bunch of people who never voted for anything before is not going to help.
Narratively, his advice is largely unrealistic. Most governmental systems are organic. Concepts like Divine Right was not conceived in some round table, but politics between the political class and the religious class. Over time, leaders start to consciously use it to their advantage, but that's a different story than a guy telling the King that he should declare he is chosen by God when there's no historical or theological precedent (though also narratively, there are actual gods that may give actually their blessing, unlike real life when even for the religious, most can agree God is not conferring special authority).
And also it's just weird to for a character brought from the modern world to suggest it. Maybe it's just a Westerner's mentality (and Japan is a democracy despite still having an emperor), but there's too many historical drawbacks versus successes in justifying authority by God. If he aware enough of the concept to suggest Divine Rule, then he's aware enough to know its dangers. It would be much more fitting if his advice expand on what he suggested for two sentences: separating tax collection and the military from the nobility.
Also, this reminds me of a book that fits well to this discussion; Something Almus, the author, and we all should find to be a good read: "The Dictator's Handbook: Why Bad Behavior is Almost Always Good Politics" by Bruce Bueno de Mesquita.