Maybe he isn't in mourning. Now that I read these articles, it look more like Kirk is still officially a cadet - all the others having achieved at least junior officer status. The Kobayashi Maru stunt held him back, maybe.
Kirk as a cadet, I can't buy. Kirk as a post-graduate Command School student, that's possible. I just don't think the crew is
fresh out of the Academy. I can accept that they're at a point before WNMHGB, but not just out of the Academy.
Even if it is a reboot, they're clearly keeping some aspects from TOS, so I can't imagine why the story would need the entire command crew to be from the same Academy class. It just doesn't make sense to me.
I see rank braids on McCoy's sleeves, and Scotty and Sulu's, too. It looks like McCoy has the 1 1/2 braids of a lieutenant commander, and that Sulu has the single braid of a lieutenant. If they're all fresh out of the Academy, they'd all be no-stripe ensigns.