Reportedly, one of the reasons the novel's method of euthanasia was changed to Carousel, was thanks to MGM's Soylent Green (1973), which used a method of euthanasia very similar to that oroignally created for the Logan's Run novel. As a result, the film's producers did not want to tread on the same ground as a recent film (despite the Heston film's alleged swiping from the Logan novel), so the more visually spectacular Carousel ritual was developed for the film.
And that's fine to a point. It's a film, so there needs to be some spectacle and flair. The thing is, the stakes and purpose are poorly addressed.
Again, not a problem if it's just some kind of blood sport done purely for entertainment, noting more. However, "last day" and the chance of "renewal" are central the character motivations.
Its a closed system, but in the film, the fact there were underground groups of runners with their own weapons implies the city has always had a crack in its perfect system, allowing unsanctioned assembly, manufacturing of weapons and probably drugs. "Muscle" was supposedly developed to enhance physical performance, so like real world steroid use would become on a larger scale in the 1970s - forward, "Muscle" probably started off as a drug developed for commercial use, but fell into a peddled drug status, skirting the law or any monitoring system.
Except as per the script it's no good for anyone over 13. So who's making it and who's giving it to the delinquents and why? There doesn't appear to be any economy to speak of, so it's probably not just for personal profit.
What's really going on here is that the story wants to portray an allegory of the perceived irresponsible youth, middle class hedonism and delinquency present in the real world, so they're just dropped in this future setting without any real thought as to WHY they're there within the context of that world. That's lazy writing.
If you're referring to the film, one can assume Yellows--like the rest of the age orders--have their structured training/place, to (ultimately) become part of the hedonistic class (the average citizen), skilled workers (e.g., Doc and Holly at the New You shop, the clean up crews who remove human remains, et al), or were already selected before birth to become Sandmen.
All well and good, except, again the movie never gets into how this society works, which really is kind of the whole point of doing a future dystopia setting. 'THX 1138', 'Brave New World', '1984', 'Hunger Games' etc. all go to great pains to explain how and why it all works. It's necessary in order to convey the point of the story...which as I said is kind of the core problem here: there really isn't much of a point, just a lot of vague flailing about youth culture.
Really speaking I think the story says a lot less about the follies of the youth of the 60's & 70's at which it was aimed and much more about the fears of the adults of the time. The war generation that felt themselves becoming less and less relevant as they saw the boomers grow up in a world (in their eyes) so much easier and free of hardships.
"synth" score? You should listen to Jerry Goldsmith's full score again, as any synthesizer parts are minimal at best, with the rest being one of Goldsmith's greatest works, and one of the best from a decade with a boatload of great soundtracks.
That's as maybe, but I typed that not a few hours after watching the movie and the synth and random beeping noises are the only parts that made an impression, hence: unmemorable.