I like mythic narratives and I know that a lot of my games have involved a sort of 'save the world' drive to the action. But the point of the plot is not simply saving the world. It's creating some sort of positive change in the aftermath.
I mean, ultimately "saving the world" is just the broadest scope of heroic action. Swap out something else for 'world' and you get tons of adventures covered in one broad stroke. Save the town (which is the most important place in the world to its inhabitants). Save your family (who mean the world to you). Save the kingdom. Save a business from financial ruin. Save a play from sucking. Narrative has conflict, and removing the threat that provokes the conflict will pretty much boil down to 'saving the X' most of the time.
What matters is what the peril is, how it matters to you, and what consequences your actions have beyond the end of the story.
I remember the first D&D game I ran, The Night Below, where aboleth are trying to mind control the world. I enjoyed it, my players enjoyed it, but it made for a mediocre story because you never had time to see the world that you were saving. The plot spent so much time in the underdark that you never had a chance to get attached to anything else. In writing War of the Burning Sky, I wanted to make sure the players got to know the world, and got exposed to lots of people from different walks of life. I put in opportunities to work with numerous allies, and to turn some enemies into friends. That way, by the end of the whole saga, when you the heroes are going to defeat the leader of the evil empire, you have already made an impact in the world. You have to care about it, because in a way it's your world now.
Of course, along the way there is epic heroism and astounding action, mysteries to plumb, history to reveal, and memorable vistas, all of it to make the world distinct and alive. But I also ran a game based entirely in a small town, which focused on the people and lands right around it. At the end of that story, the players cared about their home, so even though they just stopped a small band of marauders, they felt like they'd saved the world.
Anyone can tell a story about saving the world. It takes some talent to make the world (village, kingdom, business venture, theatrical production) cool enough that you want to save it.