To the thread's question, I'm torn. SNW is a prequel, so I expect, and often like seeing, ties to TOS. I enjoyed the fourth season of ENT the most of that series because I felt it was finally delivering on being a prequel to TOS. That said, I do feel that Strange New Worlds, as well as Discovery, are misnamed. Like I feel that there's been very little exploration, or discovery, on said series, I also feel that SNW doesn't give us enough actual strange new worlds. It's like the creators have been given the keys to a cherished toy box and they can't help but play with toys they've wanted to for a long time, instead of delivering on the promise of the series title. Being a prequel, and not even one that has almost 100 years of space between them like ENT and TOS limits their options, as well as the use of legacy characters that were later on TOS, but I would like to see them flesh out and stretch out what space they do have.
I think Hollywood's, as well as the audience's receptivity to nostalgia, also factors into it. People have liked the Easter Eggs in the past, and Hollywood has poured them on. Now it feels like Hollywood just slathers on nostalgia without seeing if that's what the audience is still as receptive to, or is demanding.
I think it should be a balance. There's nothing wrong with honoring a franchise with a storied legacy, though at the same time, I think SNW should strive more to stand on its own, so that newcomers or casual fans will understand what's going on, or why a said character or bit of dialogue matters without having to go to Memory Alpha or have it explained. Being very nostalgia driven I don't think will bring in new people, which defeats ultimately whatever Paramount's plans are to expand the franchise.