The President is being a bit of a dick about it, but she's not wrong. Did Burnham choose wrong in this instance? Maybe. Have we seen other captains make similar, or even more ill-advised decisions and have them come good? Absolutely. The problem isn't what she did, but why she did it.
Which is not to say the President was innocent either, for someone who's supposed to be assessing Burnham for another command, she just can't help throwing her weight around, even after she seemingly acquiesces to letting Burnham be in charge. Thirty seconds of grumbling every time Burnham makes a decision adds up, maybe everything would have gone smoothly if the Workbee had launched earlier.
On the other other hand, the captain should not be the one to walk off the bridge in the middle of a fluid situation like that, even is she is apparently the best person for the job. Detmer is presumably better, but she's trying to keep Discovery from crashing, so it's fine she's out, but is there nobody else?
And that's not to ask the usual question when 'the transporters are offline' comes up: isn't there a bay full of shuttles that have their own transporters? Also, isn't there a bay full of shuttles?
Minor nitpicks are the uniforms that are somehow less flattering than the TMP ones, complete with a rank badge that is both useless and must be extremely uncomfortable; the 'lol politicians suck' bit feels too much like Picard not really understanding what the Federation is; the fact that Spock's Axiom and the Kobayashi Maru aren't the same thing, they're just linked in that situation, why does nobody who riffs on Wrath actually understand it; and the fact that there's basically no scene where the camera isn't moving.
I know I'm harping on about one thing, I did actually like most of the episode. The pre-credits was a bit frenetic, but felt good, as did the rescue mission in general It all felt like people got to contribute to solutions, rather than just be props that go 'Aye sir' occasionally. I liked Tilly's breakdown on the station when Nalas pulled the phaser. I liked the quiet scene with Booker's family, even though I gave it 50/50 on it being a 'look at the happy people we're going to kill by the end of the episode' and I hate that I was right about it. But overall, yeah, enjoyed. I hope they can go up from here, rather than the down that's been the general trend.
