I've met plenty of incredibly intelligent people in my life, and very few mentioned Mensa. Those who did had a yearning for being recognized as smart or exceptional. Perhaps using Mensa membership to draw inferences about smart people in general isn't statistically applicable. It could be that people who want to be recognized as smart have those mental issues, which other smart people don't.
I tried out Mensa briefly some years ago. I was just looking for new social circles. I have some pretty sharp older buddies that I play Go with weekly, they're a blast to talk to, and I thought I'd find some more of that. It was bad. Really, really bad. The local chapter had a tiny handful of post-retirement members. I knew a ton of folks in my community at the time, a bunch of them were smart, active people, and non…
I have seen some discussions on the internet that fit with your hypothesis that many people join Mensa to have their smarts validated. There are other ways to validate that, like getting additional college degrees. These other ways tend to result in real world achievement, like better jobs. CEOs and the like don't seem to spend a lot of time trying to get their smarts validated. They are too busy getting their business model validated.
So, I tend to see Mensa the same way you do: It primarily appeals to people who need validation they are incapable of getting via other avenues, such as pursuing their Master's or PhD.