...Does it make sense? No. But its a movie, a popcorn movie, and it is made to entertain not to follow 'realistic' change of commands, which is fine with me.
Why is this fine with you?

Why set the bar so incredibly low? Isn't it easier to enjoy entertainment that doesn't insult your intelligence?
It's interesting that you raise the comparator of the American presidency too. Military command is only one aspect of the US President's role in the same way as the captain of a Starship. Having military experience is no indicator that someone has any diplomatic, political, administrative, or economic skill and vice versa. Kirk has had almost no time to demonstrate anything other than a consistent tendency to be insubordinate! ...
I think I'd prefer to see him act sensibly once in a while and demonstrate the efficiency of his crew in sensible ways a bit more often.
Excellent point. Kirk in the TV series was willing to take risks, of course, but not generally wild-ass uncalculated ones. As much as I loved (most of) the original-crew Trek movies, I think one of their shortcomings is the way they reduced Kirk to a shorthand version of his younger self, always ready to defy Starfleet, steal ships, and go off half-cocked at the drop of a hat. It helps raise the stakes in any individual story, of course, but over time it also creates a pattern that seems problematic... and this film takes that and amplifies it by an order of magnitude. Or two.
He's reduced to a caricature of his original self, really. I recognize that one of the maxims of Big Movies is "defy authority," and there are certainly times and places when that's thematically appropriate, but it ignores what Kirk represented in TOS. He
was the authority figure, after all... and notwithstanding his (very) occasional need to sidestep a self-important Admiral or somesuch, he kept in mind what that meant. He represented law and justice and a consistent set of principles "out there."
I fear that I'm coming across as some sort of status-quo worshipping authoritarian here, which couldn't be further from the truth. What I'm trying to get at is this: Kirk as we knew him
earned the trust of the people around him (above and below), and thus his authority as Captain. He didn't get it handed to him as a result of luck, or chutzpah, or even Destiny. That's all changed now. One big win on one big roll of the dice simply
does not mean that he has what it takes to do the job long-term.
(Except, of course, that he will anyway, by dint of Writers' Fiat.)
And oh, FWIW... any sort of analogy whatsoever between Jim Kirk and George W. Bush kinda makes me throw up in my mouth a little...