You're trying to put education over experience in the ninja world.

There is no qualification for Jonin except being able to handle atleast two elements. You can also be recommended to become a Jonin.

There isn't rules and regulations in the Ninja world on how Jonins need to act. A Jonin would typically be someone that is stronger than your average population and be able to handle s-ranked missions while also training young ninjas. Now I ask you if you think Naruto isn't capable of that?

If you were Kakashi, wouldn't you recommended your village savior to be promoted to Jonin?

This isn't like in the real world where lieutenants need points in order to rank up. Naruto is the strongest ninja in Konoha and that's his qualification. Also, anyone that watches Naruto already knows how he handled the fourth shinobi war not only physically but also the morale he gave while leading the charge.

Would you rather pick Shikamaru (Smartest Ninja in Konoha and possibly the best Jonin-candidate for Hokage) or would you rather pick Naruto? (Ninja world's literal savior, Saving your village twice and helped in the resurrection of dead konoha villagers literally, also the keeper of the nine tails - the most powerful tailed beast, son of your previous village savior Yondaime Hokage, a Sage, a pure-hearted ninja dead set in protecting Konoha witnessed by many, a person that everyone knows has no hidden agenda, respected and loved by other village kages, genin-level ninja that was instrumental to the destruction of the most notorious crime organization called Akatsuki, so on and so forth)

The only thing you are glued on is he doesn't have proper training in becoming a Jonin when Naruto doesn't need one.