Maybe he just hasn't "become" Kirk yet. He is already making decisions based on both logic and his gut, which is Kirk, he just needs to do more thinking outside the box. Maybe that develops later in his career.
This is my thinking. The Kelvin timeline had us thinking Kirk was always KIRK. But perhaps he's not, and KIRK is something Kirk has to evolve into. Considering he's only a lieutenant now (which never happened in Kelvin), he has time.
It's almost like they're giving him the Picard treatment in how he rose in the ranks.