I'm sure it has as much to do with nostalgic connections as its positive view of the future, plus fascinating storytelling with good camaraderie between the characters. My initial awareness was kids swapping "Star Trek" gum cards in the 60s but it was a show that aired after 8.30pm on a weeknight in Australia, so I was in bed.
I remember loving TAS in b/w on Saturday mornings in the 70s - and some eps of TOS that were specially selected to celebrate the arrival of colour TV in Australia in 1975. One of those eps I caught was definitely "The Devil in the Dark" - very memorable for so many reasons. I wish I could recall exactly which others, but possibly "Miri", "Arena", "The City on the Edge of Forever", "The Trouble With Tribbles" and "Spectre of the Gun". Certainly, McCoy's blue eyes were riveting; my whole family was fascinated with them.
Then I managed to avoid totally the huge "Star Wars" phenomenon of '77. I'm not sure why I didn't bother with it - because I really liked science fiction - but I'd just started teachers' college and I guess I was distracted by my studies (and all the related social aspects, such as writing and performing in skits, and representing my group on committees). But, in late 1979, my course was over and suddenly I needed something to do, especially since we'd been told to expect a four year wait for a full time job offer.
On the night of my 21st birthday party, a friend described his recent attendance at the gala premiere of ST:TMP. The cinema had been filled with people in costume, and I'd just been reading a series of newspaper articles about the "making of" this reunion movie that had reunited the cast. It suddenly became a "must see" movie. I bought the novelization, which I couldn't put down (I certainly hadn't planned on getting to the end before seeing the film) - and then used a birthday voucher to buy the soundtrack LP before getting to the cinema (no friends or relatives wanted to go with me, so I went alone) - and wow!
Within a few weeks, the potential void in my life left by my college graduation was suddenly filled with similar social aspects. I found local fandom: and I was again writing and performing in skits, making costumes, collecting and reading "Star Trek" models, hunting for "Star Trek" novels, new people to meet... and so on.
ST:TMP was a life-changing event for me. From then on, each new "Star Trek" movie, tie-in and sequel TV series was an adventure of anticipation, discovery and nostalgia.