I used to believe Star Trek was plausible as a teenager growing up watching it, until I watched a few documentaries and read a few books (The Physics of Star Trek), that set me straight.
These things are relative. Compared to the sheer, ignorant nonsense of most other SFTV from the '50s-'80s,
Star Trek's moderate degree of scientific literacy was a major improvement. Hell, at least
Star Trek knew the difference between a star system and a galaxy and knew that you couldn't reach other star systems on rocket power alone.
Science fiction doesn't need to actually
be realistic. It is fiction, after all. It just needs to sell the illusion convincingly enough that the audience can suspend disbelief and buy into the fantasy. As long as you include enough plausible details that the audience trusts that you know what you're talking about, then it's easier to get away with the more implausible bits. The audience knows it's an illusion, but it's a convincing enough illusion that they're willing to play along.
The technology is just over the top fantasy-transporters, warp drive, so many worlds with sentient life...
Like I said, using warp drive to reach other star systems is a lot more plausible than using an ordinary 1950s-style rocketship to do it, or just somehow drifting there on the Moon after it's been blown out of orbit like on
Space: 1999. At least using warp drive recognizes that the speed of light exists and that other star systems would be years or decades away without FTL, which is more scientifically literate than
Lost in Space or
Battlestar Galactica ever were. And even though it's unlikely to exist in reality, the concept of warp drive arises directly from Einstein's equations of General Relativity. It's called "warp" drive because it's based on the principle of altering the topology of spacetime, i.e. warping it. So it is a scientificaly grounded concept -- not in the sense that it can realistically happen, but in the sense that it arises from a real physics theory rather than just being some made-up thing.
As for an abundance of worlds with sentient life, there's no reason to think that's implausible. The "Rare Earth" hypothesis may have been fashionable a decade or two ago, but it's been largely discredited by all the subsequent discoveries about the ubiquity of Earthlike exoplanets in stars' habitable zones.
No, the most implausible thing about Trek's portrayal of alien civilizations (aside from them being humanoid) is how many of them are at a technological level within a few hundred or a couple of thousand years of ours. If anything, statistically speaking, most would probably be millions of years ahead or behind, or at least hundreds of thousands if we assume a planet goes through repeating cycles of civilizations or of new sapient species' emergence.
The Expanse has a different problem, it has a believable future, but the scientist/doctor characters are evil, I suppose Alex Kamal (pilot) and Naomi Nagata (engineer) are somewhat inspirational characters.
Prax Meng was a good-guy scientist. And there were the guys in the ship studying the construct on Venus, before their ship got disassembled. I'd expect there to be some decent scientist types studying the Ring in the current storyline.
