@Hussar, I basically agree with you but look at it through a slightly different lens. I'll try to explain.
Without going full Marxist - I'm not a Marxist, though would consider myself at least a bit of a Marx scholar - there are fairly significant relationships between technology, living standards, modes of government etc. Eg if your economy is predominantly subsistence and agricultural, with most people having to grow their own food through predominantly manual labour and reliant on natural conditions for successful harvests, then there will be famine from time to time, because sometimes there will be floods or droughts or locusts or whatever that affect the harvest. And there will be members of extractive hierarchies (eg owners of land on which the agricultural production takes place) who will probably
not be the first to miss out. Conversely, the more the economy has the sort of technological capacity to make the production of food a specialist activity, with a high degree of control over degrees of surplus and the distribution of surpluses, the less it will look like Ye Olde <whatever> and the more it will look like a modern market economy.
The same sorts of systems of social norms that tend to justify hierarchies in a society with little social mobility - which a predominantly peasant society is likely to be - will also tend to push against norms of political equality, free choice of occupation, etc. While our FRPG worlds are full of guilds and the like, just as you say we pay little attention to their role in controlling access to economically desirable social roles - although breaking up guilds and related monopolies was one of the central elements of the French Revolution!
I can't comment on Icelandic democracy, which I know little about. But Athenian democracy rested at least in part on the relative independence of the citizenry. And this flowed, at least in part, from economic independence which was made possible by (i) individual citizens themselves owning slaves to help them with their work, and (ii, and probably more important) wealthy actors in the economy being able to satisfy their labour needs by way of slavery and hence not bringing the poorer, but nevertheless independent, citizenry fully under their control. And the mechanisms that substituted various sorts of non-slave peasant labour in much of Europe after the end of the Roman Empire tended to produce both the social relations and the social legitimation frameworks that I mentioned in my previous paragraphs. (On Athens, I'm relying on MI Finley's work.)
But in typical FRPG worlds we posit peasant societies with romanticised versions of their social hierarchies (noble knights, benevolent kings and prelates, etc) without slavery, where the legitimation frameworks and economics systems value individuals, and seem to permit free choice of occupation, etc. And to the extent that anything more "feudal" is mentioned, we just pretend that it won't make people suffer ie we just ignore the implications of unfree labour, extractive hierarchies, dependence upon natural conditions for sufficient food supply, etc. In this respect we follow soundly in the footsteps of JRRT, the Arthurian storytellers, certain romanticised conceptions of American frontier yeoman democracy, etc. But there is a tendency to ignore that these imaginary worlds are at least as unrealistic and impossible as spells and dragons!
