I'm advocating for logic classes and philosophy of argument classes at the primary and secondary education level. Even with this training, it wouldn't guarantee everyone would be more logical, but I would hope that more children are exposed to the formal teaching of logical arguments, fallacies, and potential self-scrutiny of their own arguments or objective (non-emotional) evaluation of others' arguments. I didn't recieve any formal logic education until college, but in was very interested in the subject. I think by exposing people to this subject, we could at least have some sort of positive impact on maybe 20% of the population - say the ability to identify strawman arguments or red herrings that I see quite often in the clickbait headlines of articles.

Yes, education in general, such as the PhDs you mention, would not necessarily be helpful in this. The current education system tries to teach logic and argument implicitly through assignments dealing with other subjects. Unfortunately, I think this can lead to the inclusion of biases such as teachers being bias towards answers that agree with their own. For example, in third grade I said a bath is more water efficient than a shower because you could reuse the water in the tub for other purposes and you don't need to fill it as high as most people do. My answer was marked wrong because they were basing the answers off the stereotypical ideas of baths and showers.