That would have been a really bad idea.
You know who did reach back for the "general style of TOS" and did it successfully in a modern way was J.J. Abrams and Bad Robot, for the nuTrek films. What they were consciously trying to do, though, was to evoke the kind of mid-century "cool" of the original Trek's aesthetic; the movies are retro and nostalgic.
(Aside: I'm gonna get tired of "aesthetic" when everyone else has finally done with "iconic.")
The intent with Discovery does not appear to be in any specific way nostalgic; they're really at least trying, a little, to bring a contemporary look and feel to the show. This is why I think it may be more distressing, as it unfolds, for very conservative fans than the nuTrek movies ultimately were.