This whole meme hinges on a single line from Gary Mitchell, told, not shown, and it’s even followed up with “I knew I could distract you from academia with that little blonde lab technician”. Kirk’s hardly dumb. An example might be when he engineered gunpowder to kill the Gorn, or his battle of wits with the Romulan commander in Balance of Terror. But usually a broad description of someone like that captures their most prominent trait, and Kirk does not project himself as an intellectual. In fact, having recently rewatched TOS, his leadership style is more swagger and bullying than thoughtfulness.