i am thinking perhaps a showdown between the dads will determine this once and for all because that is where all of the headmasters warped views come from, his jealousy etc..
It isn't jealousy. It's reverence. Azami revered Jouichirou as the most amazing cook ever. But then for reasons Azami couldn't understand, Jouichirou quit that life and instead became a father and an owner of a small diner. Azami decided that was because of how free and different cooking could be, so he wanted to create a world where all cooking was decided on by the top, and the ones below that would just have to follow the recipe to make perfect gourmet dishes, rather than innovating on anything.
When is the man in question going to make his appearance?