Not necessarily. We still tell stories about Hercules and King Arthur and Rama and the Monkey King and the like centuries or millennia after the original tales were told. Because they kept getting retold and reinvented for new generations and new audiences. .
Difference is that unlike those stories and/or those characters, the TOS crew were first realized through the medium of TV and thus first represented by a particular group of actors. This isn't like Batman which first appeared in a comic book to then go on to be played by various actors. This isn't Tarzan or Sherlock Holmes who first arrived to the masses through books long before actual actors would portray them. Kirk and Spock were identifiable to the masses just as much by who played them as they were by what the characters stood for. And there is nothing wrong with the concept of letting the characters pass away from the movie and TV mediums at least when the actors are no longer capable of playing them. As many issues as I have with the prequels of Star Wars I pray we don't get some reboot after Lucas passes away. A reboot with new actors playing Han, Luke, Leia, etc. That smacks of unoriginality and it smacks of the greed of companies to want to keep cashing in. What is wrong with simply allowing the characters to live on only in the written word?
If Star Trek can't keep its brand alive without going to the well again and again with Kirk and Company showing up in films then perhaps it needs to be put out to pasture for awhile in terms of TV and film. I will argue that TNG's success was in large part because Star Trek had been off the air for 20 years and the population had become hungry for new material again. But when Paramount decided to immediately followup TNG with DS9 and then VOY and then ENT, it ended up diluting its most precious franchise. Hell, even TOS needed a second chance to capture the audience's imagination which it got when its episodes were rebroadcast in syndications years after it was cancelled. Shows and franchises need time to breathe. Why give DS9 a try years after it leaves the airwaves when you have four other Trek series to choose from? The same for VOY and ENT. It's overkill.
Here's another sobering thought: despite the critical acclaim of JJ's recent Star Trek film and the overall approval rating from audiences, that film did not become the worldwide smash that you would hope it would have become. It didn't do SW business or Harry Potter business or Spiderman business. Maybe it has a chance of following the route of Chris Nolan's Batman which produced a first film that made a respectable amount of business before going big time with a second film that brought in crazy amounts of box office cash. And ask yourself if JJ's first film has created a large group of new fans who have now been turned on to sampling the TV series and the novels? Was ST's popularity at a peak after that film was released or during the height of TNG's popularity? TNG, a show that used new characters and new stories to not only preach to the converted Star Trek fanbase but to bring in a new generation of Star Trek fans in general. If the new films can't do this then the franchise ultimately still needs an infusion of new fans to regain that level of success. Otherwise all you will have perhaps is an occasional movie that can make decent money but not enough of a fanbase to sustain Trek novels or other Trek merchandise.