It is probably an interesting and relevant question why not.

I agree; this is an idea I would like to hear someone else's opinion on. My intuition is that teaching people logic and science has nothing to do with making them better people; it makes them more effective at whatever they want to do, max. Trying to teach "being a better person" has been attempted (for thousands of years in religious organizations), but maybe not enough in the same places/times as teaching science.

Also, the study of cognitive biases and how intuitions can be wrong is much more recent than the Enlightenment. Thinking that you know science and all your thoughts that feel right are right is dangerous.