It's the same level of justification for TOS level tech in the future as when "Lorca kept it dark" was why season 1 was so dark, insofar as the lighting never got less dark. It's meant to brush aside discrepancies with a very specific thing applied to a broad set of values. Unfortunately, it only serves to draw attention to those discrepancies. I don't give a hoot that DSC doesn't look like TOS, as far as the show itself is concerned, and this kind of dialogue drags me out of the episode more than any visual discontinuity between DSC and TOS ever would have.
The idea that people only hate S31 being in the open because they aren't willing to go with the narrative of DSC is just plain silly. It's making people with legit criticisms into: "you only hate it because it's different, you just don't understand, it's too smart for you" kind of nonsense. S31 being in the open isn't bad because it's contradictory, it's just not nearly as dramatically interesting as the clandestine organization as it was presented in DS9.
It reminds me of how the creators talked about why they set the show before TOS and a big talking point was the "creative shackles of so many years of Trek" and the ethos that if they made a sequel, it would be hard to keep all the random Memory Alpha tidbits straight. What they were ignoring (willfully or not) was that those same "creative shackles" apply to a prequel as well, and if anything even more restricting if you want to fit it into the existing universe. Not that they need to make it fit. It would be fine if they did their own thing.
Now we have a scene where Number One talks to the audience and assures them there will not be any of those pesky nonTOS holograms in the future. The reason I don't like the holograms is because they are boring (though that might not have been the case if they were implemented better) and they distract from the scene (ie Sarek hologram sitting on a surface where he is not - sure, many have explained it away, but I don't want to even be thinking about it in the first place).