Their obsession with the Starfleet insignia is a little strange. It strikes me as similar to people flaunting their flag as if to say "look at how patriotic I am," except that it's "look at how 'Star Trek' our show is." In the first episode of STD that you mentioned, Burnham acted nothing like a Starfleet First Officer would, so drawing the insignia in the sand was one of the few things that told us that we were actually watching Star Trek.
I think it's also part of trying to making Star Trek "cool". They need a cool logo.
If you think about it, it doesn't even make sense because in NuTrek Starfleet is basically evil and often the antagonist.
I think that they're afraid that emphasizing space will limit the appeal. In the 80s and 90s, they emphasized space in the marketing and most of the films took in around $100M each, which was profitable, but nowhere near the $300M+ of a Star Wars or Indiana Jones movie. Nowadays, they want something that attracts more than just a niche audience of nerds, which I think has something to do with them casting an actress for Discovery that was in The Walking Dead, a show that has the kind of wider appeal that they crave. I'm afraid that the days of Star Trek being sci-fi for the sake and love of sci-fi are basically over and it's now just a vehicle for Paramount to exploit for commercial and social reasons.
It seems like there's a space based movie every other year that does really well. I mean obviously Star Wars is a space film as well.
Some years back, I was listening to a Bob Orci interview where he discussed writing Into Darkness. On the subject of studio interference, he said that Paramount had told them Star Trek movies feature Earth prominently do better than Star Trek movies that don't.
Anyone who actually knows Star Trek, understands that it's just a coincidence. But corporate-studio-think is "Star Trek has to have Earth in it".
Thus ST09 and STID are earth based and ST marketing materials de-emphasize space.
It's also the reason for the Yorktown space station in Star Trek Beyond. It's a stand-in for earth. Prior to making the movie, Paramount marketing research showed one of fans biggest complaints about the prior two movies was lack of deep space and exploration. That's why the movie is called "Beyond". At the sametime, Paramount still wanted Earth in the movie, so the compromise was to create the Yorktown Space Station as a stand-in.
The rumored script for the 4th NuTrek film involved time travel, and I'm pretty sure the plan was to go back to Earth as well, where Kirk would meet his Dad.