Which part is controversial? The fact that DSC has a much larger budget than TOS? The fact that DSC has 50 years of lessons learned from science fiction television production and technological development to draw from? Or the fact that Discovery's visual effects and costumes are of a much higher quality than those of TOS? I see nothing controversial in any of those statements.
Your capitalized word "IMPROVEMENT"—that's the controversial part. Obviously, a lot of us find the visuals in DSC to be less aesthetically pleasing than those in TOS.
Certainly the budget is higher, and the FX technology is more advanced. But that doesn't necessarily mean the actual visual results are better to look at. The FX tech would be at 2018 levels no matter what design choices were made, after all. In fact, there's actually a whole separate thread discussing how the FX in DSC are actually inferior to a lot of other contemporary FX work (with comparisons to shows like, e.g.,
The Expanse), not necessarily due to the talents of the FX house involved (which is apparently quite good), but due to specific creative choices that come from someone on the production side, like the high-contrast shadows, the lighting blooms, the omnipresent blue sheen, the surfacing and window boxes of the starships, the cluttered spacescapes, and other technical details.
But mainly, what I'm talking about here are the designs. DSC is at its best when it sticks closest to the TOS visual aesthetic — with things like the phasers and communicators and the engine room. The more it diverges from them, the more unsightly it gets — with things like the uniforms, the
Charon, and (at the nadir) the redesign of the Klingons and their ships. At least, that's my take. I
like the look of TOS (always have), and so do a lot of other people. So making a blanket statement like saying DSC is an "improvement" is, yes, controversial. One might as well say "Star Wars has a better visual aesthetic than Star Trek" and expect people to swallow it.
What story elements are you actually referring to, then? ... To be honest, I can't think of a single thing that happened in Discovery that doesn't fit extremely well into TOS given that series' overall lack of world-building...
Gee, it's like you haven't read the thread at all.
You mentioned three that (you surmise) the producers were talking about because they imagined they were the primary areas of fan concern: Burham's family background, the Klingon War, and the continued existence of the spore drive. I already explained that Burnham poses no actual problem, and hardly anybody here has claimed otherwise; that whatever problem the war did or didn't pose, ending it didn't make a difference, and there's no putting that genie back in the bottle; and that the spore drive
does pose an issue for future continuity but the producers seem to be in no hurry to address it, as they already gave themselves an excuse to write it out and then closed that door on themselves.
Beyond that, other posters have mentioned quite a few things. For example, the widespread use of cloaking devices a decade before the Romulans surprised everybody by having them because they were considered only theoretically possible. The widespread use of point-to-point intraship beaming when a decade later it was considered a risky trick for emergencies only. The widespread use of holographic comms when those weren't previously seen in Trek until a century later. The widespread knowledge of the existence of the Mirror Universe when it was apparently completely unknown a decade later. The tech level seen
in the Mirror Universe, which is at odds with it being comparable to the Federation's a decade later. The apparent invisibility of either of the two types of Klingons we've seen before, even though showing them would
improve the backstory about internal divisions in the Empire. The conversion of Harry Mudd from a sleazy con man to a brutal killer. The fact that Starfleet's admiralty, the Federation Council, and Ambassador Sarek(!) were depicted as being hunky-dory with putting a mass-murdering psychopath in charge of a cutting-edge starship and using genocide (or the threat thereof) to resolve a war. And I'm sure I'm forgetting a few... people have called attention to so many!...
Sure, it's probably possible to cobble up rationalizations for most or all of those story elements, and even for the visual stuff. I've seen 'em in this thread. But the more rationalizing you have to do, the more you have to squint when you watch the show and do mental somersaults for it to make sense, the more you have to ask whether it's worth the trouble. That's the central question that runs through this whole thread.
For my part, as I've said, I do still include the show in my headcanon, as part of (what I consider) the "prime timeline." But it's an open question how many of its details I'm going to have to elide in the long run to keep doing that. (And if it keeps doing shark-jumping episodes like Lorca's heel turn or painfully contrived ones like the season finale, that'll only
underscore the question of whether it's worth the trouble.)
And I'm not even going to touch the notion that TOS was deficient in worldbuilding. That's just ridiculous on its face.