But we've also never really seen the details of how a ship transitions from one captain and crew to a new one. This is an opportunity to depict how Starfleet ensures continuity of command and crew cohesion when something happens to one of their captains.

I like seeing that there's a system of mentoring and intership collaboration in place so that when there's a sudden shakeup in the crew roster it's not an unforeseen calamity but just another eventually they all trained for. Presumably this is happening all across the fleet, and it could well be that Kirk is doing this with several other ships as well as part of his command track.

It only seems strange because we know he's destined to take Pike's chair. He doesn't know that. He's just learning and absorbing all he can about how different crews function.