Your question seems to be implicitly assuming that most great teachers could also have been great engineers. At the risk of stereotyping, I do not think that i

Your question seems to be implicitly assuming that most great teachers could also have been great engineers. At the risk of stereotyping, I do not think that is true. A great teacher must be dynamic, engaging, intelligent, able to connect with children so that they can teach creation and innovation. But an engineer must be intelligent, methodical, and able to master vast amounts of technical knowledge. I suspect most people who make great engineers would not make great teachers, and vice versa. There will be some that could easily be great at either though. Those, I think would better serve society by going into engineering for a few reasons. One is that the number capable of being a truly great engineer is smaller than the number capable of being a truly great teacher. Both are significant for society, but one is more rare than the other. Also, it seems that the point of education is to be able to produce great makers such as engineers who do the work that holds society together. If we always direct our best minds to enhancing the best minds of the future, we will have highly educated children but little or no actual progress for those children to enjoy.