Schools are information environments, so there is already precedent for trying to improve the education level of society along some metric.
Eg schools where most students leave believing political violence is acceptable should probably receive less funds than those that emit students who are trained in the art of argument.
As the US finishes transitioning to a low trust society, it’s worth considering how one would introduce changes that would return us to a high trust society in 100 years or so.
If misinformation exists, enemies of a state will spread it.
It’s a reasonable solution to consider taxing pollution and using funds to clean up the externalities.