It is easier when it is clearly a new take on something. Like basically any new superhero movie with a new actor, director and producer (and sometimes even studio). Its expected it will be different each time there is a new Batman that some things will be quite different because its been like that even in the comics for decades. Yet still Batman has a clear bat motif going on in most of his stuff.
Star Trek doesn't have that particularly without an excuse given by the film or series itself. Kirk and Spock were recast in 2009, but it was made clear that it was an alternate timeline and some serious things changed since the day Kirk was born...so changes were acceptable (more or less). Discovery hasn't yet recast (or even shown) Kirk and Spock, nor any of the main cast of any of the other Star Trek shows. They've recast Sarek, but Mark Lenard is quite dead, as is Jane Wyatt for Amanda. It doesn't take place on the USS Enterprise, so they have not redesigned that (yet). The slate was, mostly clear as the time period is the 2250s, and they so have some things that are similar in style and color to things that would be normal in Star Trek set in the 2260s. Otherwise changes have been because time has passed in the series. USS Enterprise gets a refit and its been a few years when TMP happens. TNG takes place almost a hundred years after the Five Year Mission. ENT takes place over a hundred years before the Five Year Mission. The largest changes were makeup related, and details related, which were passed off as "bigger budget" and generally accepted on that basis, with hints of the passage of time, or multiple sub-species of said races in story resulting in the changes (and for the Klingons, resulting in the virus and cure result some decades later). However, during the last 50 years, until Discovery, some things did not change when certain eras were revisited. If a set looked like it did in 1968 on Star Trek, than it still would look more or less like that because time hasn't changed inside the universe to alter the appearance of something seen in 2268 for anyone else seeing something from 2268 again. That's just how it looks and that was accepted all the way through to the end of Enterprise in 2005, and elements of Enterprise made it into the new films. Name dropping have happened in Discovery, and some of the visuals still potentially link into the era. The big, "but" is the Klingons. Now the Klingons have had their appearance changed before for a larger budget, but there shouldn't have been a reason so do that again, just because of the budget. That seems like a waste of money verses something that worked for 20 years post-TMP and to the end of Enterprise with modifications and refinements. Plus the actors could work with that makeup effectively. Add to this the Klingon starships are all sorts of random doesn't leave a good taste in one's mouth. So far the only logically reason I've heard as a rumor for the heavy makeup was to potentally keep the identity of a future Klingon spy a secret before they show up without the Klingon makeup (like if they introduced Arne Darvin as a Klingon cultist, then he shows up later as a Federation official, with the new makeup you won't easily be able to tell they were the same person because the actor is so covered up and sounds different wit their teeth and usually speaking in stilted Klingon.).
Now things might still fall into place somehow. The more traditional Klingons, could appear later one, or the Klingon makeup will get less busy over time. The Klingon starships might become less ornate and more industrial and functional for the war effort.