It's hard today to imagine SF in the 60s. It tended to be blown off with the derisive "... that 'Buck Rogers' stuff". While there were some standout SF pieces made before Star Wars, they were few and far between, and were defacto shielded from public consideration by the unrelenting sort of dreck which becomes the heart of MST3k episodes. On TV, before ST:ToS, of quality SF there was The Twilight Zone, and little else (maybe The Wild Wild West). Gene Roddenberry first pitched ST to CBS, which turned it down, because they already had a Sci-Fi show (only room for one per net, you know) -- Lost In Space
Then ST came onto the air, and, for the first time, Space Exploration wasn't about "rokkit ships 'n' rayguns", it was about people exploring strange new worlds, seeking out new life, and new civilizations. In short, it was about what Man will be doing if we ever get off this planet.
More importantly, it showed a future with promise, in which humans had begun to rise above our petty, earthbound squabbles (which contrasted sharply with the Doom and Gloom which arose in the Seventies, thanks to The Club of Rome and supposed "geniuses" like Paul "I've never been right on a single prediction, but still people listen to me" Ehrlich).
ST did more than just establish SF as a serious genre. It broke spaceships out of the rocketship or saucer mold, which virtually all ships until then had been.
Yes, we look at the show today, and the FX look pretty cheesy, but, in their time, they were utterly groundbreaking. It would take 10 years and more of development in these areas to produce a Travelling Matte (allowing for non-static FX shots) and the "chest burster" scene in Alien.
In reality, there were many things which we still haven't come close to producing, such as the sensor beds, the tricorders, and the needle-free hypospray (closest to reality but still not there yet)
The writing of the time was often some of the best then available, and literally sparkled compared to much of the writing found on TV ("Ward, don't you think you were a little bit hard on the Beaver last night?"), and, although the third season plots suffered as a result of the knowledge that the show was on a slow drip to death, the latter first season and second season episodes could still be remade with only a small amount of rewriting and still be enjoyable. It was good despite the fact that it is very difficult to be a good movie writer, a good SF writer, and a good fiction writer all at the same time. That essential synergy is one reason for all the dreck Sci-Fi masquerading as SF. Writing good SF instead of Sci-Fi means writing good fiction despite the easy out of rayguns and rockets. Writing good SF requires enough understanding and appreciation of science to realize that it's not enough to just invent a double-talk generator to solve your problems, you must have that DTG have a reason to exist in the first place (one weakness to ST:TNG was the tendency to use Wesley to make the DTG at every turn, hence the universal SF fan hatred of the Wesley character -- he made for bad SF).
Further, writing good SF for TV or even movies requires understanding the limitations and capabilities of the venue. You may be able to blow up 500 starships with a few clicks of your keyboard, but the FX department has to fit that into their budget for the show. The pacing for a TV show has special requirements, as well. It must (especially in the 60s, less so today) break the story up into a specific pattern, and all the appropriate ideas, actions, and plot points must fit into each pigeonhole "just so".
So looking at ST with this realization, it had to do all these things, and do them for the first time -- there was no "classic Star Trek" for people to point to, and say "I want to make something that impacts people like THAT!" -- And you will start to see and appreciate why ST was, in every way, the Einstein of SF on TV (with The Twilight Zone as its Newton). Don't look at it with today's Matrix eyes. That is neither fair to it or fair to your understanding.
Try and see it for what it was in its time -- a magnificent flight of imagination, an impressive breadth of vision, and a incredible work of art. If it falls short sometimes of perfection, remember the Waltzing Bear -- it's not how well it waltzes, but that it waltzed at all.