This was one of those instances where going by the book of Starfleet was a BAD IDEA. In the original series, they never really get into how DIFFERENT Klingons and Romulans are from Terrans. They are ALIENS.
Which was why there was always friction, not just between Terrans and these other races, but a three way tension, Klingon against Terran against Romulan against Klingon.
So far, in this show, the Klingons are not the Lovable and ridiculous GOWRON brand. These are truly ALIENS. Not the safe kind either.
What you don't understand, can kill you, until you DO understand it.
That's what happens here. Michael understood, but being raised Vulcan makes it difficult to express immediacy to one's captain. And Georgiou was not getting it. Until the end, maybe. But then it was just more bad luck.
This is supposed to be Starfleet history. Somewhere in this story is Captain Garth. and Axenar. Which explains CBS's lawsuit, the fan film was about ready to spill Discovery's entire plot line. But we haven't gotten to Garth yet. Maybe Sovol is in this universe, hanging with Sarek. And they are both putting up with irritating humans.
But where Axanar was being assembled to tell the story in terms of the old Universe of Trek, using the designs we had been familiar with, with actors playing the people they played in the shows, this version of the story is telling the tale from the outskirts, from the Fringe Division of Trek. Why are there holes in the Discovery's Saucer Section? Oh, WAIT. You have not seen that yet. Well, you will, and then you will see why.
This is the Section 31 version of Trek History. Which does not make it bad in any way.