If you're going to maintain the episodic nature of these things, i.e., each one stands alone, then you really can't have much change in the characters and settings. Otherwise, you're doing a story arc, and you're either going to require your audience to watch everything, or spend a lot of story time on exposition to catch up those who didn't see the last one.
And if a segment of your audience didn't care for the last one, then building on what you started on the last one just made it that much harder to sell to those who didn't like it. At least with all the playing pieces put back where you started, you're starting with more of a clean slate and the disaffected are a bit more likely to give the next one a chance.
Change in a series does not alway constitute a "story arc" and doesn't require having watched the previous outing nor does it require that the next one be built upon it. The change can be. In fact, you can have change and deal with it without lengthy exposition.
A talented writer can easily show such things or dispatch it with minimal dialogue. And clever dialogue can also convey what the audience needs to know without the audience feeling like they are being
told exposition. Take the
Lord of the Rings trilogy. A lot of the exposition was handled quite deftly through the dialogue and actions of the characters.
Book series have been doing stand-alone adventures that continuously change characters and settings for a long while. For instance, John Scalzi's
Old Man War series. Each book is basically stand-alone, the characters and setting changed, and whatever is built from the previous books is dealt with rather quickly through a minimal amount of exposition. Just enough for the reader to "get it" about the universe and move on.
Granted you have a great deal more space to deal with such things in a novel than you do in a motion picture.
But let's use a
Star Trek example:
The Voyage Home, easily the most successful of the original TOS movies in terms of bringing in a wider, more mainstream audience. The movie built on what happened in
The Search for Spock. Yet that picture basically told a stand-alone adventure about picking up a "couple of humpback whales". The bits of change from the previous movie were dispatched in a scene that used visuals--i.e. the record tapes--to convey what happened. And audiences still flocked to that film, sitting through the expository bookends.
Emphasis mine
Of course, this all works better for a tv series; every show has a bad episode from time to time, and maybe next week's will be better. With feature films, everything gets exaggerated, because of the time between offerings, and you're charging money; much easier for unhappy audience members to respond with, "Get stuffed!"
The time lag can be an advantage to a clever writer.
Time has passed, simple as that. Riker is here now and Troi is there. Picard is on the
Enterprise. They've moved on. Or there are new characters. And so on. You just start with them in these places, you don't really need all the interstitial steps on how they got there, and if you do, once again, it can be dispatched through tightly-written dialogue. Kinda like the start of TMP. Of course, that movie in the end restored the status quo.
Of course, Trek has the perfect exposition device--the Captain's Log.