Not sure specifically why TNG, DS9 and Voyager went seven seasons, since TNG and DS9 were both first-run syndication. Voyager was off-network syndication, but I do not think you need seven episodes worth of material for that (it is usually 65 or 120 episodes to coincide with 13/26 weeks of Mon-Fri broadcasting). I mean Enterprise went into syndication with only four seasons under it's belt and TOS did it with three.
They intended
TOS to run for 5 seasons, hences the "it's 5 year mission to explore strange new worlds." It got axed for low ratings.
Enterprise was also axed, due mainly to bad writing. Scott Bakula isn't a good enough actor to work with a weak script. I thought he was great in
Quantum Leap, but then that show had some good writing.
I can see Discovery getting the axe because it is very expensive and Paramount+ is likely spending a mint getting Star Fleet Academy off the ground (the main set is said to be the largest every constructed for a television series).
Disco suffers from the same thing a lot of remakes of great movies/shows suffer from: they get compared to the classic. The wrong kind of "improvements" infuriates the old guards. When the remake idea bombed, the went completely off track...which should have drawn attention from the temporal agents for temporal shenanigans.
Why don't studios do remakes of movies/shows that had promising premises, but bomb due to poor F/X or writing. Remake
Manos: The Hand of Fate with a real script and real actors.
This is what endured
DS9 to a lot of fans. They made the Ferengi--a purtided attempt at replacing the Klingons--as a fun species whose antics in
TNG could be blamed on a series of misunderstandings.😉
But Lower Decks is far cheaper to produce...
And far better.