It already does, in broad strokes. Roddenberry always saw ST as only the best approximation of the future that present-day production methods could achieve, which is why he didn't hesitate to redesign everything in TMP. In his foreword to the TMP novelization, he pretended to be a 23rd-century TV producer and apologized for TOS's inaccuracies in dramatizing Kirk's adventures, saying that TMP was a more accurate and authentic recreation. So if he were still around and involved in making SNW, he would've been the first to redesign all the sets and tech and claim that was how it had really looked all along.
After all, if we can accept Jeffrey Hunter and Anson Mount as the same character, how hard can it be to accept the TOS sets/FX and the SNW ones as the same ship?
If anything, I think SNW goes too far in duplicating details of TOS, putting very 1960s intercoms and rocker switches and "jellybean" buttons as decorations on the otherwise modern touchscreen consoles. I find those overly literal recreations incongruous and nonfunctional. I prefer it when they recreate the broad-strokes aesthetics with more modern detail.