Fair question. Why do I need the excuse? Let me consider this in terms of both personal emotional implications, and the logic of fictional continuity.
On an emotional level, it's because I relate completely to what WebLurker posted a few pages ago: "TOS is the primary foundation of the prime universe. Everything else builds off of it or to it. It's arguably Star Trek in its purest form. It's a respect thing." Original Star Trek, that ship, that crew, is what I fell in love with long ago, and without it as the foundation I really wouldn't give much of a damn about the rest of the Trekverse. There is no spin-off series that would have hooked me strictly on its own merits. Episodes of latter-day series that show honor and respect to the original are among my favorites (e.g., TNG's "Relics," DS9's "Trials and Tribble-ations," ENT's "In A Mirror Darkly.")
Therefore, anything in the franchise that undermines it, or purports to replace, displace, or alter it, had better have a damn good excuse.
On a logical level, it's because I appreciate and care about continuity in my fiction, whether TV or film, comics or prose. How consistently a fictional setting hangs together and builds out its world matters to me within any individual story, and even more within a long-term shared fictional setting. Things that violate internal continuity draw attention to themselves and disrupt my willing suspension of disbelief. The larger the violation, the larger the disruption. Yes, of course, nobody's perfect and no continuity is flawless... but it's an ideal to shoot for, a limit condition to approach asymptotically. Therefore, if some story within a given fictional reality sets out to change major aspects of that reality, it had better have some logical in-universe rationalization for doing so. (When DC Comics decided to reboot its universe in 1985, for instance, it devoted a high-profile year-long series to doing so... not to mention months of build-up beforehand. And if such things are to be done, that's how they should be done.)
As applied to my impressions of DSC, and the topic of this thread in particular... I have a lot of issues with the show. Storywise, I've enjoyed some episodes and disliked others; it's a very mixed bag. The same goes for the characters, and the acting, and the designs, and pretty much every aspect of the show. Lots of pros, lots of cons. To the extent that the continuity poses problems (in terms of visuals or narrative or both!), that's just more in the "cons" column. To the extent that the continuity fits with what came before, or at least can be rationalized to do so, that's less of a problem.
(FWIW I probably wouldn't have phrased the OP's question as "is it Prime" any more than "is it canon," because "Prime" is just a handy marketing term devised to describe what ST09 diverged from, and to my mind previous Trek continuity has involved a number of (usually subtle) changes in its timeline over the decades. However, by and large they all fit into a fairly coherent reality... and terminology aside, the intent of the OP was clear enough. One of the things that made DSC sound so interesting in concept, when it was first announced, was the opportunity to visit my favorite period of that reality (or something very close to it). Insofar as it's instead something very different from it, that's disappointing. Insofar as it's different enough to undermine the coherence of that reality (or at least that part of it), that's more of a problem.)
How's that? Less baffling?
And given that, I'm grateful that they provide a handy in-story excuse for completely segregating them from everything else that is Star Trek.
