I'm not a fan of Star Trek, but curious - where are all the stupid & lazy people in their universe? Ie have they been bred out, are they back on Earth and the show doesn't dwell on them, or what?
Probably back on Earth (or whatever their homeworld is).
Besides the issue of being theatrically-fulfilling, the nature of something like Starfleet would tend to select against having truly stupid/lazy people there. Even the modern (and for that matter, WWII) U.S. submarine fleets are not cross sections of society, and the technical and training requirements would only seem to have gone up for Starfleet.
I'm presuming the "bred out" thing didn't happen, since the Star Trek canon (and a few episodes, e.g. of DS9) speaks of eugenics as a practice becoming highly disfavored hundreds of years before the events of the various TV shows and movies.
With all that said it is definitely implied that life in the Federation is essential utopian, without lazy/stupid people. Maybe a more knowledgeable Star Trek geek can explain how the show explains it but AFAIK the disparity is never explained by anything more substantial than improved social policies after First Contact.
For the life of me I cannot remember, it may have been in some DS9 episodes about Dr. Bashir. But I believe it was stated that eugenics had effectively eradicated a lot of social ills before the issue of genetically-augmented superhumans led to the Eugenics Wars.
Honestly the takeaway of this is that questions like "do you want to live in Blade Runner or do you want to live in Star Trek" don't work because Star Trek is more fantasy than science-fiction when it comes to how some of that stuff works.
We can't literally live in Star Trek's universe because, so far as we know, the laws of physics don't allow FTL travel. But, there are numerous elements of Star Trek's society that are worth trying to achieve, even if we don't have to go about achieving them the same way the writers envisioned.
As others have mentioned, it's just fiction. It's not a roadmap to a destination; it's encouragement to build that destination ourselves.
Since utopia is implied you can assume the population is healthy, well-fed, well educated (possibly for free), and has a low crime rate across the board.
This alone would pretty much ensure there are no lazy/stupid people. Stupidity is largely a factor of health and education, laziness mostly a factor of social norms (encouragement, expecting success, role models etc.)
What I'm saying is that on average people behave the way you expect them to as long as they know what's expected.
IQ (as one imperfect measure of intelligence) is significantly hereditary.
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Various studies have found the heritability of IQ to be between 0.7 and 0.8 in adults and 0.45 in childhood in the United States.[4][7][15] It may seem reasonable to expect that genetic influences on traits like IQ should become less important as one gains experiences with age. However, that the opposite occurs is well documented.
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Don't you think that stupidity is a relative term?
Ie every society will have 50% of the population that is below the average intelligence. And the lower quartile be considered outright stupid - because the rest of society is not tailored to their needs.
The Star Trek of the Kirk period was transitioning into a post-scarcity economy. By the time Picard was captain, money was no longer in use. When you have replicators that can make anything you desire so long as you have the schematics, who needs to trade for anything? People were free to choose what to do with their time.
