The different Trek series are different stories. The fact that they are vaguely related and occasionally refer to one another doesn't mean that they're beholden to one another. The writers can do as they please. They select material from other series as it benefits their artistic vision and disregard what doesn't benefit their artistic vision.It is a foundation-level element of competent fiction writing to make sure that things presented within the story make sense within the story.
The so-called Prime Timeline is a marketing term. It's an arbitrary corporate designation for a series of different but somewhat related television shows.If you're serious about insisting that there is a difference, you're basically looking at the whole question at the head of this thread and saying not only that DSC isn't in the prime Trekverse, but that no such thing as the prime Trekverse even exists.
Every Trek series after TOS is a spinoff of TOS. The subsequent series are free to pick and choose what they like and disregard what they don't like. Each show is its own entity and its own unique story with its own aesthetic and design choices.
TL;DR Star Trek is a set of different but somewhat related tv shows. The writers and artists of the day can cherrypick as it pleases them and suits the unique story they're trying to tell. Canon and timelines are arbitrary marketing definitions. None of it matters. It's all made-up.