I think your explanation is possible. Not sure if I agree with it, but I can at least follow your reasoning.
What I question immediately is that the idea that continuity is valued in the MCU because it was designed that way. If sf audiences as a whole had little concern for continuity, then designing an interlinked entertainment to have high continuity wouldn't do much to sway them. If they didn't like continuity in the first place, they'd probably ignore it, maybe bad mouth it (although I tend to doubt that), but they wouldn't praise it. Yet, among fans and (what I'll call) casual fans, and reviewers, continuity in the MCU gets high marks. I don't think designing it to have high continuity would change minds among people who don't value continuity in the first place.
On the other hand, if sf audiences as a whole valued continuity, then it would likely be valued in Trek, but based on the general comments here it isn't (and I would consider TrekBBS to be a reasonable cross-section of Trek fandom).
This leads me to believe that there's a fundamental difference between Trek fandom and MCU fandom. I find this odd as well, as in my experience most fans are multi-franchise fans, which on the surface would make it likely that a majority of Trek fans would also be MCU fans.
Here's where I think we are at a crossroad: I do not think there is a black and white between Trek fans and MCU and valuing continuity or not. I think, as
@BillJ notes, there is a large spectrum. As the joke goes, ask ten Trek fans what they like about Trek and you'll get twenty different answers.
I can only speak for myself and my observations. Continuity is something I care about in broad strokes, and generally within a contained work. So, the MCU isn't something I am overly bothered about the continuity of because I just watch individual films. I just recently watched Dr. Strange for the first time, and prefer his individual story over the stupidly large Endgame that I had to turn off. But, I can appreciate the level of effort put in to the MCU to build up that continuity, even if that isn't why I watch it.
With Trek, that's a different animal. I never expect Trek to have continuity as that went out the window with TMP and TWOK. It simply had different variation, even if the broad strokes were somewhat consistent, i.e. starships, transporter, etc.
I think that continuity in the MCU gets high marks because people recognize the work and effort that goes in to it. My favorites authors right now are Jim Butcher and Brandon Sanderson. Now, these two writers put a lot of emphasis on continuity of their worlds. Sanderson is ridiculously detailed oriented and intergrates multiple books series under his collective universe. Now, while that is not the reason why I enjoy his stories I can certainly appreciate the effort put in to make that possible.
Continuity, for me, will come down to "It depends" in terms of importance.
I'm also not sure I go with your last last, that the MCU feels similar because it feel inflexible. It's pretty well established that the people behind the MCU went to great lengths to make sure that it all fit together, with Endgame in mind from the beginning. That being said, consider how many different tones and styles had to mesh in Infinity War and Endgame, not to mention plot details. Just adding the Guardians of the Galaxy was a feat. If someone had told me, when the MCU was first starting out, that the could have pulled that off I would have laughed (too tonally different than, say, Captain America), but overall I thought it worked. So, I don't think it feels similar because it's inflexible. I think it's incredibly flexible, and was made to feel similar, i.e., canonically consistent, through skill.
And that skill is appreciated. But that's not the base conceit of Star Trek.
As for being inflexible, I'm not talking about tone. I am talking about how the story progresses. The MCU feels like a giant train that is chugging right along its tracks and come hell or high water it will arrive at its "Endgame." If a character isn't important enough to warrant appearing in that ending then you can be sure he'll be left by the wayside, regardless of continuity. Things like "The Defenders" just don't get a part of that despite popularity.
Now, contrast that with Trek. Trek went from DSC with plans for S31 to Picard and Strange New Worlds. There was flexibility in what stories they wanted to tell based upon audience response. The MCU just keeps chugging along regardless.
That's what I mean by inflexible. If it isn't in the plan it gets binned.
