For one thing today’s science fiction fans are a lot more tech savy and therefore far less willing to tolerate technobable, hand-waved explanations and general inaccuracies. Star Trek was created before the World Wide Web, average viewers were less likely to realize that much of the series’ so called science was pure fantasy. This was fine at the time because they mixed some real science in there and got a lot more people interested in the subject who wouldn’t have been otherwise. Unfortunately for Trek the end result is an audience less willing to accept bad science in their entertainment. If Star Trek: The Next Generation were first airing today Neil Degrasse Tyson’s twitter feed would accumulate so many factual corrections it would collapse in on itself and form a digital black hole.
More importantly people today are too cynical for a show like TNG. Today's viewers increasingly don’t believe in the idea of a more positive future hence the prevalence of dystopian and post apocalyptic novels, films and TV shows. The most optimistic space operas of today, like The Expanse at best operate with a sort of “same shit different century” milieu. The world isn’t dramatically worse but not necessarily better. Many of todays problems such as racism, sexism, homophobia, religious intolerance, and war on Earth don’t seem to exist, but new ones have cropped up including corporate oligarchy on an unprecedented scale, interplanetary cold wars, exploitation of Belters, and OPA terrorism. Star Trek’s technological utopianism and humanism wouldn’t resonate with modern audiences, who are increasingly distrustful of technology and jaded about human nature.
My life does not revolve around a silly pocket telephone. But I feel like Kevin McCarthy in "Invasion of the Body Snatchers", or Vincent Price in "The Last Man on Earth"--the only unafflicted human left, surrounded by pods.
No one cares about the techno babble. These shows are set far in to the future in a fantasy world. The technology needed to for Star Trek to happen obviously doesn't exist. The techno babble helps the fantasy sound plausible. But no one watches Star Trek expecting it to be realistic.
Neil Degrasse Tyson is apparently a huge Star Trek fan, so even he is able to suspend his disbelief and the enjoy the shows for what they are. He would only tweet about it if they got something wrong with black holes or super novas, he doesn't care about warp drives or photon torpedoes, there is no real science there.
TNG works because it's character based first and foremost. The storylines while based on topics of the times, are disguised, and explained well enough within the star trek world, that you don't need to understand the times to enjoy them.
I agree with you that anyone who watches the show wouldn't have a problem with the technobabble. I don't think that would be a barrier today.
I think a bigger problem if this show were to debut today is the greater discernment of the viewer to logical inconsistencies and continuity errors.
Part of it is due to the connected world we live in, where we all share our criticisms and observations immediately and extensively. The other part is the DVR and streaming, where we can instantly rewind or re-watch to review a part that just doesn't make sense.
In the 80s, you would typically watch in real time as it aired and move on, so there wasn't much opportunity for the scrutiny that shows face today.