Yitz, could you please comment on Bava Basra that has no problem with fathers teaching children, except that many fathers were not capable. Nowadays, when many communities have fathers who learned for many years, it is hard to argue in favor of disenfranchising them: either yeshivos teach well and then father are now certified to teach their children, or they do not teach them, and then there is no reason to send kids there! In truth, there are a number of pro-active parents who are in chinuch who try to teach classes with their own kids.
For a general picture, I don’t think we are an “autocracy”, I think we are a distributed system that includes respect for learned and moral authority. Those Rabbis who set curricula get funded by parents and donors, who choose who to sponsor. Our most venerable poskim acquire that position by the virtue of you asking your local Rov, he sending some of the harder questions to his Rosh Yeshiva, and Rosh yeshiva sending his hardest question to whomever he considers most appropriate to ask (that particular question). They are not (currently) appointed by a Sanhedrin.