I also think there are a lot of products that hijack the need for cognition, to make people feel like they're achieving something when they're really not - for example dense complicated games like Factorio/Satisfactory/Dwarf Fortress/Paradox games have all at one time completely taken over satisfying that cognitive need.
While I see what you're getting at, I take issue with your main point here:
> So they are sort of scratching their itch for cognition, but not in a way that makes their life better in an objective way (which is most likely the reason we have this drive)
Evolutionarily, there is no such thing "the reason" why we have any drive. Rather over time certain characteristics are selected for by their fitness in the environment. That might seem like a semantic or not important distinction, except that this drive for cognition has effects way beyond the individual.
The key thing is these people who go after what most would consider "unproductive" things, IE not using their smarts to go after lucrative professions, serve an important role in society to break out of local maxima and ultimately bring society to entirely new places. But this drive is obviously not a precise tool, it is just as likely to go towards some non-productive ends as productive (the cognitive equivalent of junk food or whacking off).
Some people simply have a larger drive towards cognition than to social status, and that occasionally leads to changing the world.
(Footnote: this is simplified - obviously evolution/selection happens on the individual level, but as a society we place value on intellectualism because of the outsized impact, which alters the environment to select for this drive - and people often reach their achievements later in life, so the "evolutionary success" of having kids is based on their potential for greatness, even if they never reach it. This way selection can favor drives that actually hurt most individuals with the drive, because the ones that change the world have such an outsized impact - this only works because humans are adaptable enough to alter their selection criteria based on the broader environment - think fat people used to be attractive when nobody had much food)