Manbearcat
Legend
You hardcore narrativists never have much sympathy for we humble vanilla narrativists!

As far as D&D alignment mechanics are concerned, in the sort of game I'm envisaging they all have to be dropped. The mechanics, and even moreso the cosmology, and even moreso the cosmology as read through the lens of Planescape, tend to assume that both law and chaos are compatible with good (and so both Olympus and the Seven Heavens are equally good; and both a dwarf and an elf will register to Detect Good; etc), and hence to assume away the very conflict that I am positing as the focus of the game.
A unilateral GM power to change PC alignments based on the players' play of their characters would also be at odds with a narrativist game.
When I talk about using 9-point alignment I'm certainly talking about the descriptions, not the traditional mechanics.
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I think you're right that resolution mechanics would need to be robust, but (given my vanilla proclivities) I don't think the mechanics in question have to involve the sort of reward-for-theme you describe with Inspiration (though nor would your suggestion do any harm!). I'm envisaging a game in which the GM throws out challenge that raise the whole question of wellbeing in connection to social order or its absence, and the players (via their PCs) make action declarations whose resolution pushes things one way or another, both towards or away from wellbeing, and with or without respect for social order.
I've actually worked on hacking a Founding Fathers/American Revolution game (with multiple systems) where positive and negative liberty would be in conflict, and in the midst of that conflict shape the face of revolution and deal with post-war fallout. Most of the time the questions of such things require some form of revolutionary imperative or responsibility of rulership by the PCs (or both). Playing a game where you're on Thomas Jefforson's transformative philosophical journey through revolution and rulership would be quite fun!
Imagine if your paladin Thurgon had rallied the people, defeated the dragon, and restored order, security and prosperity. It is clear that the once goodly king, without a suitable heir, is unfit to rule and maintain that order, security, prosperity. What if it is the will of the layfolk, the clergy, and most of the military that Thurgon claim the throne? What then? Does Thurgon claim the throne with the full knowledge that it will come with a hefty price of further destabilization, bloodshed, an estranged ruling class, and general misery with a kingdom already heavily taxed.
What if Thurgon is then faced with the supernatural pall that is seizing the Iron Tower? If that order of knights isn't restored/helped, who will stand against the always encroaching evil of the untamed borderlands? But there are barely enough soldiers to man the ramparts, as is. Does he re-institute an ancient, unpopular decree to conscript all able-bodied males over 14 in the city and the outlying homesteads? Perhaps there is an executive branch check...maybe a senate where proposed proclamations of war or inquest are debated. Does he unilaterally suspend standard government procedure as a war measure?
What about the refugee problem? And the infrastructure problem? And the problem that the entrenched nobility expect a standard of living, protection, and benefit that is well beyond the means of the post-war crown?
In order to have a functional narrative gaming experience, all of those questions need to be sorted out in play. If the place of Law and Chaos is already established before play (1), then play has become pointless. If the resolution mechanics don't allow for player agency and the snowballing of conflicts such that their fallout distills the answer to the question of the relative merits of Law vs Chaos, through play (2), then play becomes pointless. D&D has historically struggled with 1 due to the constraints of established cosmology. D&D has historically struggled with 2 due to insufficient/incoherent resolution mechanics/PC build tools (such that players can actually and authentically "move units" in play), insufficient player buy-in (typically due to lack of focus and lack of reward/feedback system) and the substitution of GM Force (upending player agency and the "play to find out what happens" angle) where the prior two fall short. Solving 1 and 2 are key imo (4e certainly did its fair share of fixing 1 and 2).