Trek is most definitely an utopia. That is its key defining feature. As I just described, utopia has nothing to do with a static paradise or a naive vision and more to do with the everyday struggle to improve and it doesn't exclude what you called 'going through hell'.
Gotta disagree with you there. The original series was much more about exploring strange new worlds and encountering exotic alien life-forms than painting a picture of utopia. Heck,we never even saw
23rd century Earth in TOS or really heard much about how it worked. Just the occasional bit of lip service about how mankind had progressed since the bad old days.
To my mind, there's a difference between optimistic and "utopian." Trek stands out because, unless most scifi series, it's not
set in some dystopian, post-apocalyptic future where robot cyborg gorillas have taken over. It's set in a future that works,
where humanity didn't blow up and get conquered by alien invaders, but when you go back and look at the original episodes, they're mostly about running into salt vampires and sexy female androids and Doomsday Machines and so on. Sure, there's the occasional speech about how much humanity has grown, but that wasn't the gist of the episode. And we were just as often told that humanity was still a half-savage child race with a long way to go.
TOS was actually very suspicious of seeming utopias. Pretty much every time Kirk ran into some "perfect" world, there usually turned out to be an evil computer or mind-warping virus involved! Utopias always seemed to involved sacrificing some degree of humanity . . .
But I digress. Bottom line: to my mind, STAR TREK is primarily about exploring the Final Frontier, not some portraying some vaguely-described utopia back home.
Just look at the opening spiel. It begins "These are the voyages of Starship Enterprise," NOT "Welcome to the Utopian World of the future . . ."