I can say that having been through a similar curriculum in high school (implemented on the initiative of a very thoughtful literature teacher) it has been one of my most valuable mental tools I possess throughout my adult life. Being able to understand and identify logical fallacies has helped me critically evaluate the information I consume many times over.
Of course, any program like this has the problem that it needs to be implemented by a trusted source, or it will be attacked as "indoctrination" (whether or not that is the truth). I can see that as a major challenge in the US where 50%+ of the population is convinced that the government is out to get them at any one time.
A lot of school curriculums ostensibly include critical thinking skills because this is seen as important, but don't tend to teach this in practice.
Classes tend to focus on how to jump the hoops of getting good grades (without accepting any critical analysis of the grading system).
Are you then really teaching children to be critical, or really teaching them that it's best to conform to what they are told? It becomes difficult to teach children critical thinking skills, because of the way schools are presented to them as an objective authority.
I think this work can be done, however - and is most often done by lone wolf teachers acting alone and outside of classroom norms. That's certainly my experience.
You just need to frame it correctly.
The explanation was that people with some education become prideful and believed they know more then they did, easy targets for gullibility. But people lacking education had often street smarts and was less susceptible. And the ones with phd:s had learned how complicated things really are and was often reluctant to take a hard opinion about things they did not know much about.