There's no evidence that it does stay stable- the author is making a lot of assumptions about the 'implied setting' of OD&D that aren't really supported by the game materials at the time. 40 silver pieces couple be 40 Roman denarii, 40 pre-1965 US quarters, or 40 chunks of a silver bracelet. They could represent the pocket change of a dungeon builder, but be a considerable sum to the barbarian that finds them. The implied uniformity is just because the author lacks imagination.
Even in the US, "free silver at a ratio of 16 to 1" worked - at least somewhat - by government fiat, not commodity value. (Great, I've now got the urge to write "Gresham's Law" while I flash back to high school history class.)
So I was ready to type "it's just a game", but the truth is OD&D isn't even really that- it's a set of mechanics from which a games master could select in order to make their own game. How closely you wanted to hew to the socio-economic truth of the 'Medieval period' was 100% up to the GM. "Chivalry and Sorcery", "Empire of the Petal Throne", and "Runequest" were all games that tried to implement more 'realistic' simulations of pre-modern society that came out soon after to specifically address D&D's lack of setting detail.
"'The Tempest' as an allegory for European colonialism? It's just a play."
My comments in this thread concern textual evidence which cast doubt onto A_D_E_P_T's proposal that "The only rational way to interpret D&D is not as medieval, but as a distant far-future post-post-industrial setting."
I found the thesis that OD&D draws from US expansionism to be interesting. The fact that later games tried to implement more realistic simulations is besides the point.
In fact, the essay author observes that by doing so it takes away from the 'American fantasy of empowerment and upward mobility' which was perhaps 'the last un-muddled example of the genre it inspired'.