Yeah, I agree, more practical things should be taught in school. Finances / money management, the laws and legal rights where they live, etc. We have physical education/health requirements...why don't we have mental education/health requirements? Financial education/health?
I can see your point in indoctrinating people through a system that way, and systems do often have a pattern of becoming more corrupt over time. I think that's in part because corrupt people are attracted to power, but regardless of whether that's actually why, the indoctrination is indeed a vulnerability. We've already seen some issues in schools with misinformation about historical events and figures, etc.
One problem I see in this though is that I think that a lot of people are already resistant to influence in general, thus causing soooo so many people to get stuck in unhealthy behaviors and decisions, repeating the same issues throughout their lives (which is also in part caused by lack of education). Without knowing what to look for, people might just become fearful of or rebellious against outside influence, including in negative ways, just simply because it's influence, which is what we're already seeing with the refusal to wear masks. While I do believe being sheeple / having a cult mentality is a real problem that should be addressed, I don't think independent thinking necessarily addresses the root of the issue enough, and a lot of people may think they're making their own choices and that they're simply agreeing or showing support or something without being aware that they're being influenced. I think it's important for people to start making more informed/educated decisions, too, or to be aware of when/how they're being influenced, but that just ties back into people being more educated about mental health.
If part of independent thinking involved educating yourself more, then you have the problem where there will be a lot of faulty resources and misinformation that is ingrained in people who don't educate themselves properly, or in various resources put out there to mislead others deliberately. I think that if colleges/universities can handle classroom education on psychology, then schools in general should be able to also, no? I just think it's important for people to be unified in having knowledge of the most accurate information available. Furthermore, a lot of people wouldn't even value or see the importance of mental health education. You'd have to basically have a society that values education, and frankly...I don't think we have that. I think people mostly just live their lives and try to enjoy themselves unless they're fueled by pretentiousness often times. A genuine curiosity or desire for education isn't all that common, and people would have to be motivated to self-teach if going the independent thinking without standardized education route.
I also think there's a key factor at play here, and that is that in this case you're educating people about how to identify how people (narcissists, etc.) manipulate, control, etc...thus, you're essentially equipping people to recognize corrupt influence (which would backfire quite a bit if they were also a corrupt influence). I think there'd be so many educators involved that it'd be difficult to streamline corruption into it, especially since they'd be among so many others who would be trained to recognize those things (and teach others how to).