I don't think it makes more sense intuitively at all. With the vast range of physical differences we see in people due to genetics, it is not at all intuitive to me to stick to some old dogma that says the brain -- one of the most highly specialized and evolved organ of the animal kingdom -- would not have significant diversity due to genetics.

You can exercise and train your mind of course, as you can with your body. I don't see that as a plausible reason people believe this way. I think they are stuck in the anti-scientific, anti-intellectual dogma for reasons that are not rational.