For all the "Well Doctor Who or Star Wars do X" Star Trek has never done X. It has always done the update to the ship in the name of keeping it realistic and approachable for the entire audience. Making it look believable as a space vehicle as understood by the audience of the time.
From 1966 to 2018 the TOS Enterprise was the iteration that every version of
Star Trek accepted as the one that existed during the Pike/Kirk era of the ship's existence. There were refits and updates to it when they got to the movies, the newer shows introduced new stuff, but never did any of the shows feel the need to alter the franchise's past in this regard.
Even when CBS did TOS-Remastered, where they updated the effects, they could of easily said: "You know what, let's really rethink this from the ground up. Let's go George Lucas on this and bring the effects up to what people would expect for 2006." They didn't do that. They just built around the version that everyone knows.
It's not that it looks dated. It feels completely out of step with TNG and DS9. It feels...like a stage.
The TOS Enterprise "fits" with TNG and DS9 since both shows acknowledged within their own canon that it existed as part of the setting's past. Also, if we're going with which one matches the established lore of the franchise more, it's not the DSC/SNW version (e.g., Where were all the D.O.T.s during TNG's "Disaster" or any of the other episodes of TNG or DS9 where droids would have come in handy during a dangerous situation?)
Does it though? It can certainly be argued that the SNW Enterprise fits in alot better.
Within this context, what does it mean for the Discoprise to "fit" in a lot better?
If we're going to play this game, and start from a point where the argument is that we need to change this visual aspect of a story that's been a near constant for 5 decades, then everything is on the table. How can the Discoprise fit better when we're going to say everything is open to change? If that's so, then it can't fit "better" because there's no guarantee that any of it looks the same way within this vision.
For example, how do we know the NX-01 looks the same within SNW's past? Or that the Discoprise will turn into the TMP refit version of the Enterprise?