You are right, i have seen my introvert boss, taking verbal damage, hold his anger and his words for 5 seconds and unleash a devastating speech that made the other guy walk away.

He also took leading part in many high management meetings without any social fear.

I am about the middle and i hated working under an extrovert manager, all chatting, big words, self promotion stories, useless long meetings, fake friendly attitude that turned into professional talk when shit got real etc.