I mostly agree with what you said, but critical thinking can indeed be taught in elementary education. Children can learn from an early age to question the reality presented to them, to apply analytical reasoning to arrive at their own conclusions, and perhaps most importantly in this golden age of bullshit, to be extremely critical of the information they consume online, from mainstream media sources, and even their peers. Not all children will pick up this practice equally and carry it through their adult life, but it's important that they're presented with these crucial tools that can help them be less susceptible, though not invulnerable, to information warfare. Unfortunately, education is mostly based around memorizing and regurgitating facts, rather than teaching people critical thinking skills.
To be clear, we're all vulnerable to IW in varying degrees. Thinking critically at the very least makes people more skeptical of the information they consume, and lowers the chance they would spread it further and "infect" others.
There's no easy protection against IW or a quick cure from the effects of it. It takes at least a couple of decades to educate a new generation of people to slow down the bleeding, and for the oldest "infected" generation to die out. But first the nation's government must realize that they are indeed a victim of IW, which is difficult to do because there's no direct link that points to it since it's an operation that spans decades, and because of the confused state it inflicts in its victims. Judging by the actions of most Western countries, they haven't even accepted this as a possibility yet.
This is an interesting interview[1] where all this was outlined 40 years ago. So this is certainly well known to all intelligence agencies.
[1]: https://www.youtube.com/watch?v=pOmXiapfCs8