Being able to envision ST as a future, to me, is based on the qualities that made the episodes and show great, not budget and believability of tech.
What will never work for me is when the shows main conflict is how Geordi is having a hard time making a new friend. No amount of high budget computer graphics is gonna help with that. I find a lot (not all) of ST after TOS is ripe with that level of drama.
Space Seed
Amok Time
Errand of Mercy
I’d put those three episodes up against the entire Trek library of shows with their higher budgets made after TOS. The stuff in those episodes and those like it are what make me want to believe in that universe. There is little suspension of disbelief because I’ve been pulled in by the story. Good lighting for mood helps as well, something that seems to have been lost.
Just another perspective on the subject. To each their own, of course.