While she was down there, they had plenty of time to program one of the little robots to pull the lever in her stead! I'd say they are all morons.
Or the torpedo! Two minutes later they beam Spock! What's good for the goose is obviously not good for the gander.
If you want to know who was season 2's Saru's role model, you don't need to look any further than prime Landry! After all, she too thought that the confrontation between the two cons and Burnham was a necessary catharsis for the three of them and that's why she told her underling not to intervene.
I think it was just to imitate all those prison movie scenes where the guards allow a fight to go on, and those prison movie scenes are used to show that the guards corrupt and enjoy bloodsport, and that the prison is a rough place where the guards will not protect you from other inmates if it doesn't serve their interest. I don't know that there was any reason like that for Landry. They simply wanted to show that "Burnham is hardcore," and that Landry was not a nice person.
Think it was also meant to show that things under captain lorca were not being done properly or at least by Starfleet norms. Lorca hand picked a lot of his crew knowing what they were capable of on the other side.
What I don't get is why they introduced the black badges then. We never heard of s31 again before season 2.
They do have black badges, badges that can communicate like TNG badges, which means that they have devices more cutting edge than the rest of the federation by a hundred years or so. That point has been driven home enough throughout the second season.
Maybe they are ninja stars meant to look like badges... for self defense S31 would have some kind of subdermal communicators. Maybe even some kind of organic technology, so as not to be detectable to scanning devices.
Just evidence of the constant state of covfefe the first season existed in. Except we clearly see Tyler slap his badge in order to contact Leland.
That's the most random thing to go after. Neither method of communicating is really more "cutting edge" than the other. We could do that today with Bluetooth. It's just a matter of when they came into use in the Federation as a whole, and I don't see it as anything to get canon-crazy about with having Section 31 using it first. Lots of technologies get their start in military organizations before going into wider usage anyway.
*Stares longingly at liquor cabinet* It's turning into one of those threads, is it? But in seriousness, Section 31 having a comm badge a hundred years prior to anyone else isn't that far fetched. Intelligence agencies do tend to get advanced communications technology long before it's available to anyone else, even the military. Or even explorers who are exactly like the military but say they aren't.