You know, you're entitled to your opinion, but have you even watched the original Star Trek? How can Kirk leading landing parties be considered wrong in-universe?
It's just an aspect I've never really liked about Star Trek full stop, TNG took a better approach where Picard was not obliged to lead every single away team. It's just a really corny way of getting the captain character to bond with the lesser characters and to get him into the action. Having said that the TNG movies were rather Picard-centric and the ending always involved him at the climax, but I'm okay with that because I rather liked the whole; Picard is a living legend sort of thing. After seven series and some movies I thought the cliché was appropriate.
But NuKirk feels like he's only the captain because he has the pips, he bosses people around and admiral Pike made him a captain. Maturity, captaincy and NuKirk are things which are mutually exclusive so Kirk just comes off as some douche or prick for the first half of the movie.