Except that ST during that period really wasn't allowed to change its style. Unless you refer to the Bennett/Meyer movies.
People's unwillingness to accept STD as "prime" (whatever that really is, once you stop and think about it) is seeming evidence of how little change in style they are used to based on their experiences from the TNG~ENT years.
I would say that all TOS, TMP, TWOK, TNG, DS9 and eventual ENT had a very, very different style and aesthetic. Only VOY is clearly connecting between TNG and ENT. But if you look at the changes made from the original series, to the first movie, to the rest of the movies, to TNG and compare it with DS9?
That are a LOT of VERY different styles and aesthetics. Yet all of them worked together, simply because the style changed moving forward (or in ENT's case WAY backward) - You can tell literally any story you want, in any specific style you want in the Trek universe.
The only thing that always should have stayed the same, was the universe itself. But the universe doesn't dictate neither the stories, nor the style. It's just a common setting.
The problem with both DIS and the Kelvin movies is that they tell widely similar stories to what came before - but significantly alter the setting of their stories - they feel the need to alter the entire universe around their by-the-numbers stories - which absolutely makes no sense and is counter to shared universe telling.
Because that's the one only thing you should keep. The sandbox in which you can play. If you change the universe - then it's not a shared universe anymore. Simple stuff. Yet they inexplicitly did that, but still banked on the appeal of said shared universe.