My concern if DIS had been an anthology show, or if it were to become one as the OP suggests, is that it would run afoul of the same issue that "Heroes" did - supposed to be an anthology, but TPTB end up too afraid to let go of the most popular elements and/or characters to actually do it right, so they wreck the show. And yes, I know "American Horror Story" has shown it can be done correctly, but, it's also a huge mainstream hit. Which (I hope I'm wrong, but) I don't see being in the cards for DIS. I expect it to be a huge hit with fandom and a moderate hit with the mainsteam audience, as a best-case scenario.
I think you're assuming a Khan mini-series would take place between "Space Seed" and Star Trek II. What if it's actually set before/during/at the end of the Eugenics Wars?A Khan show would by nature be more akin to something like LOST (except everyone is ultra-fit and beautiful) and probably not do much to help bolster interest in space-based scifi.