^^DSN managed to keep up with the times and incorperate arc based story telling, so it isn't fair to say that Trek wasn't keeping up with the times. It might be fairer to say that some Trek shows were better in keeping with the changing times than others.
While DS9 (my favorite Trek series without question) did arc based story telling, its not the type of arc based story telling that I am talking about I should have said serial story telling.
Having events run Most of DS9 arc story telling was in either multi part story telling or picking up ideas and events from other episodes and building an episode around that. Modern Dramas were incorporating serial arc based story telling. Where events from one episode were deeply connected to parts of the very next episode. Voyage did this with the "spy" story line that was developed running through several episodes.
It wasn't until later in DS9 run that they really started doing this. Though they did do arc based story telling, just of a different kind.
Also just to point out that DS9 due to Piller and then Piller's hand picked replacement did take more risks. Though unlike Voyager (where DS9 did manage writing, and characterization about 5 times better then Voyager), it didn't push the visual aspect as much (and I don't mean a darker color palette or great CGI, just in how drama's are staged, cut, and filmed). For his weaknesses, Braga was out of those running any of the writing room, the best visual writer for Trek (and its why I wish that Ron and Braga could have continued together through their Trek run).
But it wasn't until Braga and Berman's 3rd season of Enterprise that Trek really tried a full season based serial story telling. Nearly a decade after Piller started that push to more modern story telling. And tv dramas were doing it probably 15 plus years earlier.