So here's my take: the political resolution of the narrative was so unsatisfying because the writers did not have a clear sense of what was politically defective in Westeros to begin with.
If we accept the late medieval setting of the story and the source material, however remote, of the Wars of the Roses (Lannister/Lancaster vs. Stark/York) then the political problem of Westeros should have been the independence of the aristocracy.
Sir John Fortescue's Wars of the Roses-era treatise De Laudibus Legum Angliae famously named this problem "over-mighty subjects," meaning a nobility whose wealth and military power rivalled that of the crown.
In late medieval Europe, the demographic and economic fallout from the Black Death left this stratum grasping and dangerous, squeezing its peasantry and ever pressing for more lands, titles, offices. Crowns that could not satiate these demands often fell prey to them.
This seems like a good description of Westeros: the ruling dynasty was displaced by a coalition of ambitious noble houses. And the new usurper king, uninterested in governance, presided over a long period of political drift and crown indebtedness.
From this perspective, the Targaryen restoration was supposed to stand in for the coming of the Tudors: strong, centralizing Renaissance monarchs who systematically reconstruct royal power and break the independence of the nobility.
Ok, fine. But the political rise of Daenerys Targaryen in Essos was framed in radically emancipatory terms--"breaker of chains." She's John Brown, not Henry Tudor.
This always struck me as a weird Americanism. We are asked to root for her because she is an abolitionist -- the idea being that no one would get morally or politically invested in a would-be royal absolutist.