I guess the "prime debate", at least regarding visuals, boils down to whether one views filmed entertainment as of a piece with live theatre and graphic novels/comics, or as some sort of pseudo-documentary of "reality".
Wayne Boring, Curt Swan, Jose-Luis Garcia-Lopez--these were the three main artists of Superman comics during my "formative" years reading them. Jim Aparo, Neil Adams and Irv Novick for Batman. Steve Ditko, John Romita, Sr., John Bucema for Spider-Man. (I could go on, but that's sufficient for my point.) In their respective runs, "continuity" was the same--but visually, each had his own, distinct style. Later on, the variety increased with various artists on each (some within the same "continuity", some within a new "continuity", some in non-continuity). And then there were the cross-over, team-up, or "fill-in artist" artist variations. Yet it was always Superman, Batman, Spider-Man, (fill in hero of choice). Now, most artists could sufficiently mimic another's style if that degree of consistency had been demanded (I've seen numerous examples). But, thankfully, in my view, such consistency was NOT demanded.
Making allowances for the different medium of filmed entertainment, I don't expect quite the degree of deviation seen in comics for TV shows (especially within seasons of a show). However, from one series to another, with different production teams? Why not? Dick Dillon drew both Superman and Batman regularly, but Jim Aparo's Superman (in guest appearances) looked very different from Curt Swan's Superman (and vice versa, re: Batman). Yet each was easily recognized as Superman and Batman. So too with the Enterprise in TOS, in Kelvinverse movies and now in DSC. Identical? Certainly not. Recognizable? Beyond a doubt. Given that all Trek is fiction and art, I see no reason why deviations (and, in the overall scheme of things, rather minor--even the Klingons [still bipedal hominids, who look closer to each other TMP-ENT and DSC, than either looks to TOS]) cause such outbreaks of apoplexy. I understand favouring one particular version over another (I prefer Garcia-Lopez' Superman to Aparo's, for example, but I don't have conniption fits when I see the latter)--that's entirely reasonable. I can even understand strong disappointment in a particular version (not a fan of much of John Byrne's artwork, on any title). But some of the vitriol is downright perplexing.
As always, YMMV.