I am really liking this show. It's visually cinematic and the storyline is interesting. However I still prefer traditional episodic Trek. To me this is more like Star Trek meets Game of Thrones. It's epic storytelling, but Trek works better as a weekly space adventure with longer arcs sprinkled in.
That said, this is my favorite theory...
This show is taking place in the Mirror Universe. The mirror universe is harder and more brutal so it would work. It would also explain away things like tribbles and Gorn showing up early. For me the coolest reveal in the final episode or two would be to show the Prime Universe Discovery crew in modernized, TOS-inspired uniforms working together in the more idealized Roddenberry fashion. They could also have more traditional looking, but updated, Klingon makeup, uniforms and Bird of Prey ship designs in the Prime U. The mirror crew could even switch places with their (softer) prime counterparts, cover up the crossover, and ultimately go on to form Section 31 in the Federation. Personally I think this would win over the fans and give CBS a lot more latitude in expanding the franchise with 2, 3, 4 more series set in the Star Trek universe.