Star Trek had a rough start. Not many shows that only last three seasons and get canceled twice have a 60-year run with dozens of combined films, and shows, with even more books and games. The franchise is a cultural touchstone and simply put, the flag barrier for all things science fiction. Yet, it wasn't the well-received juggernaut it would become today.
And honestly, had it gone longer than three seasons, it may not have become what it is. Star Trek has found success consistently because there is always an appetite for more Star Trek. The franchise only got three seasons, which left the fanbase ravenous for more. So much more that the show was originally in talks to come back as Star Trek: Phase II (at least the working title). Phase II didn't pick up the steam everyone hoped, but enough people believed in the brand that a film was made based on the Phase II concept.
After that, we were off and running. Films, television shows, streaming, and more have come out after the original series ended. A reality that may not have happened had it not been for the early cancelation of Star Trek in 1969. So when people talk about what shows were canceled too soon, I can't in good conscience say Star Trek.
After all, if Star Trek had gone five, seven, or even 10 seasons, like so many shows of the time did, would we have the franchise we have now? Would people have started conventions for the series? Would there be enough demand to see the film franchise take off? Or start at all? It's too hard to say but the hunger fans had after the cancelation in 1968 and then again in 1969 caused the fandom to galvanize.
That was the catalyst for a lot of the franchise's success.
So no, Star Trek: The Original Series (as we call it today) was not a show that was canceled too early. In fact, the only show that Star Trek could even claim was canceled too early was that of Star Trek: Enterprise.
The series was the second to air on UPN and didn't sustain the ratings like Star Trek: Voyager did before them. There were reasons for that. A prequel wasn't what fans wanted, the marketing wasn't good for the franchise and the folks decided to take "Star Trek" off of the show, originally calling it "Enterprise".
It made for a rough start to the series, a start that would see many fans tune out over time. Some claim it was due to oversaturation but the truth isn't that simple, nor is it entirely accurate. Fans wanted more Star Trek, as evidenced by the Kelvin film franchise starting just four years after Enterprise's final season.
So Enterprise was poised to work, but the problem is that UPN and the showrunners didn't know what to do with it. By the time season four was coming around, Enterprise was flushing out a lot of the concepts that Star Trek was built on, and a lot of historical plot points the series installed. Enterprise was now trying to fully explore the history of the franchise.
Season five was poised to be the best one yet, with fan-favorite character Shram joining the Enterprise crew as a full-time member, the start of the Romulan-Federation war, and the potential return of the first captain of the franchise, William Shatner back home.
Had season five happened, it's likely that the show would have gone seven seasons, and that the Kelvin Timeline film franchise would have never been needed.