In 1987, I recall more distinctly the book protector sleeves given out at school (in the AV club in the high school library, much to the surprise of nobody around here, and I must say the three-level library reminded me of the Engineering set, but I digress) with the season one cast. Wish I'd kept the book cover, but the instructor was happy that the book within was still in very good condition.
At first it was a lukewarm/like/dislike thing. Depending on episode, and some were baaaaad. Especially as TNG progressed and the show ditched the garbage and took itself seriously and with material that was easier to produce seriously (TNG overcame a lot at times), that's when the audience grew and ambivalence started to subside. Meanwhile I'm sitting through Star Trek V and getting all whiny over how the original crew treated itself as a joke. So did a lot of moviegoers. Fast forward a third of a century now, and one can see the movie's potential and appreciating what had worked, but - at the time - audiences were stunned after II-IV, but not by the special effects and not in a good way. Ditto for TNG, as - with others - I've gravitated toward seasons 1 and 2 as the 90s went by, and often returned to seasons 1-4 far more than 5-7, with some exceptions. Earliest TNG really did feel most exploratory, and the latter half was largely cardboard. DS9 getting the best plotting material didn't help, either. Or it didn't hurt, it depends on which series you were cheering for at that time, too...
TOS still had its iconic tone and big three. Yeah, it was 20 years old but it didn't matter. Others saw TNG as the big new shiny thing that could fix all the errors TNG had. Both sides had points and both weren't wrong. TNG proved over time that some thought could make a sequel better than the original... it did win me over or else I wouldn't have kept watching...
Keep in mind, the then-trendy issue of "You can't replace Kirk!" was very real at the time, additionally hampered more by how many late-80s shows were faddish sequels of long-dead TV shows from the 60s to recapture and build upon. See, we got to have so many timeless gems such as The New Monkees, The New Gidget, The Munsters Today, What's Happening Now, The New Leave it to Beaver, a ton of dead tv reunion movies with all of the latest trendy 80s incidental music styles (e.g. Bonanza The Next Generation, I Dream of Jeannie 15 Years Later plus another sequel, a few zillion Return of the Six Million Dollar Man & Bionic Woman TV movies, a handful of Brady Bunch reunion movies and a short-lived tv show, etc, etc), prequels such as "Muppet Babies", genuinely new series like "Miami Vice" and "Remington Steele", and probably a lot more that are stuck in my subconscious. Okay, to be fair, Miami Vice had its moments, and the New Monkees had rather decent music (if you're into mid-80s pop, some of the stuff is impressive) but dang that show itself was not the same), but I digress: With all these sequels popping up more than any average teenager's pimples as we were the target audience for this stuff, a little kneejerky reaction was going to be inevitable because everyone was expecting the next big thing to be just as stale. Then again, The Munsters Today lasted twice as many seasons as its progenitor, so there's no set rule...
The other issue, which helped, was lack of sci-fi - in terms of titles, or companies wanting to make it (or to make it good). Even TNG season 1 isn't as bad as some series from the same time period.
Will a new show recapture the "cultural zeitgeist" that TOS and TNG had? Dunno. Until then, the next best miracle is if someone finds a way to take a potato chip recipe and successfully swap potato for broccoli but with that same level of crunch everyone expects and craves, nom nom nummy-nom. Even then, they're more nutritious when steamed. So whip out the pot of water and colander, unless you can fling enough insults to enrage the floret in front of your face. Why I just wrote all of that, I've no idea... oh yeah, but then there will be a mega-super-successful show to veg out on. :9