I'm particularly interested in the perspective of a select group of individuals: Those who saw The Cage before they watched The Menagerie. That group actually numbers several dozen fans: those who watched The Cage in August 1966 at Worldcon. Was The Cage canon at that point and later invalidated by The Menagerie? Was it never canon?
People didn't think in those terms back then. TV series (and radio series, movie serials, magazine serials, comic books, etc.) contradicted their own continuity all the time. It was taken for granted that their consistency was on a global scale, the broad strokes of premise and character, whereas their specific episodic adventures stood alone, rarely affected one another, and sometimes conflicted with each other.
After all, back then they didn't have DVD box sets and show wikis and the resources we have today that encourage us to see a TV series as a unified whole. In the absence of video recorders and reliably clear broadcast signals, there was no guarantee you'd get to see every episode of a show, so each episode had to be treated as a self-contained whole not dependent on other episodes. Also, this was an age when the classiest TV shows were the anthologies, while serialization was the stuff of daytime soap operas and Flash Gordon movie serials and thus was considered lowbrow. So even continuing series aspired to an anthology-like approach where every episode stood apart as its own independent entity. Different episodes shared the overall premise and characters, but that was the extent of the continuity that was expected. When past continuity was referenced, it was often changed in the retelling, since few viewers would remember the details exactly enough to notice.
Besides, what differences are there to worry about? Sure, "The Menagerie" omits parts of "The Cage," but the only actual contradictions are the Keeper's higher-pitched voice and the different use of the closing Pike/Vina footage, and those can easily be handwaved away as production conveniences rather than in-story "facts." There's no real difficulty in seeing the two as compatible accounts of the same event. Tweaks in the details of the
telling of a story, like changing the sound mix or repurposing stock footage or recasting an actor, don't actually alter the in-universe facts of the story.