I think there might be a correlation with higher education and internalizing doctrinal assumptions about capitalism. At least in the United States. But it really just depends on what you mean. You’re talking about formal education versus just learning about class consciousness throats independent study or life experience etc…
The latter is extremely important. The former can be useful but if anything I think it will funnel more people into further accepting the deeply ingrained ideological assumptions of the elite classes.
People do seem to inherently understand that the game is rigged but they have been conditioned in a million ways to either do nothing about it or to blame the wrong people. It does require some pretty serious deconstruction to try to avoid internalizing this.
I think a good source for this kind of thing is althusser and his work on ideological state apparatuses.