No, of course you're right, the "toy model" is exaggerated. I think it was more true in some countries than others and several decades ago, when there was no internet and the media were dominated by a few players (including the government itself, in many countries) all very much established.
Let's say that I suspect that democracy is a system that assumes public opinion to be directed so that it doesn't stray too much from a narrow range of possibilities. This can be done just by manipulating the Overton window.
I disagree with the assertion that the relation is cyclical. In reality, all of these systems are highly interdependent. I'd model it as a weighted complete digraph.
And certain subsets of these various nodes have a greater outsized influence than their peers. For example, the intelligentsia within the people are usually far more impactful than say Joe Blow from Appalachia.
I’d say mass media, especially in entertainment and news (but I repeat myself), is far more influential than intellectuals, except inasmuch as they are influenced by them. But let’s be real, Noam Chomsky doesn’t have a ton of clout in Hollywood. If anything, it’s more about money than about the intelligentsia. And if you’re talking about social-media influencers, please revisit my first point.
people's choice -> government -> media -> narrative -> people's choice