The studios (and maybe public) seem to be under some misconception as to why Marvel is popular, and does not suffer burnout. Marvel is well written. It is faithful to it's origins. Kevin Feige makes sure they work as a movie first, but keeps them true to their spirit, and has fun, but does not condescend or disrespect the material. They end up succeeding because he knows their appeal was timeless to begin with, and only needs explaining again to attract people.
I'm not surprised people are burnt out on the work of other superhero franchises and studios, because they have never "got it". Batman vs Superman looks so dull and so far from what Marvel understands that I'm surprised anyone even wanted to see it; it's only the hype machine and DC brand loyalty made it profitable. They don't offer anything of what made people like comics back in the 1960s; just another washed out cynical dystopia that speaks nothing to us.
The Fox studios / X-Men series has been hit and miss, because some films like First Class, get what we want to see. But others skirt way too close to
"stop the supervillain + CGI & explosions" being their only point. Every studio has tried to copy the Marvel franchise model recently, without really understanding it; maybe only Star Wars will succeed, just because of the level of understanding surrounding it - both are also notably under the same umbrella of Disney.
I don't think you can ever suffer burnout on something genuinely good, no matter how often it's repeated. I think burnout comes from slippage in the ideals that made the thing potent to begin with. When creative talent loses their joy, their reason and creative direction - their understanding - when they get lost as to the point. It's called writer's block in other terms.
The problem from the get go with Star Trek's revival was that it was very canny in some ways, but unfaithful to the material in others. The show's TV outings had died a silent (but temporary) death in 2004, because it's creative team lost their sense of direction, after having worked on it since 1987 non-stop. The movie part of the franchise had died in 2002 because the studios couldn't even be bothered to hire a director who liked Star Trek, or understood it. Along came JJ Abrams in 2009, who was very canny in tying Star Trek to other elements of pop culture; the call-outs to classic uniforms and sets were very Marvel-like; the use of pop culture to bring revenue from other sources and streams (the Beastie Boys, Rihanna) into a franchise noted for keeping it's reserved distance from pop culture, at least opened up flows of liquidity and business confidence in the franchise. But the place many felt let the revival down is that he didn't quite understand the property as well as Kevin Feige and Joss Whedon understood Marvel, and so some of the humor came off as laughing at Star Trek, rather than loving humor, and some of the themes worked better than others. It was felt by some that the franchise wasn't being allowed to present it's timeless appeal in a new way, but being shoehorned into a different ideology, much closer to superhero reboots.
I would suggest if the films want to keep going, and from New Star Trek 3, reach New Star Trek 6 or higher, they need to perhaps experiment with other approaches - clearly fans loved Justin Lin doing exactly this, with his more Trekkie take. But how about at least trying a much more Tom Clancy-like political thriller, or Christoper Nolan/Ridley Scott-like cerebral thriller? Marvel does exactly this! Captain America: Civil War, is a Clancy political thriller. Thor: Ragnarok will probably be high fantasy. Also, what about other creative visions? While staying true to what Star Trek is, would Scott or Nolan be interested in doing one, in between Abrams and Lin's releases?
Perhaps Trek's future once again lies on TV - in learning the lessons from the movies - building an interlocking franchise on Netflix instead. Liquidity flowing in from multiple production partners. Big producers like Alex Kurtzman, Bryan Fuller, Heather Kadin and Rod Roddenbury. Multiple writing teams. More than one series, and more than one creative direction - shepherded by someone who understands it and believes in it like Feige. Unlike some cynics here, I have never had any doubt that Star Trek can be as expansive as Star Wars or Marvel - it's older and better than Star Wars - it is literally an infinite setting - it just needs people with both cunning and respect, like Feige.