Your project could benefit from increased obedience as you could just lead rationally and the others would follow.

This is a good point even for the society. To get a rational society, it is not necessary that literally everyone becomes rational. Just that the rational people make the most important decisions, and the others follow them.

Although there are dangers with this solution in a long term; specifically that some day the irrational people may decide to stop following the rational ones. In democracy it means someone else uses some simple tricks to get their attention, and wins the elecion. On the other hand, the non-democratic societies have another long-term risk, which is the leading group becoming irrational from the inside; either they lose their sanity gradually, or just a small subset goes insane and succeeds to remove the others from the inner circle.