When Frodo Baggins finally leaves the Shire, or when Harry Potter finally arrives at Hogwarts, then things get interesting to me. I outright refused to see the reboots of Fantastic Four and Spider-Man; I don't need to spend at least half a movie waiting for these mundane characters to turn into superheroes again, having just watched it happen a mere decade ago. Heroes are like meals at a restaurant: I don't mind learning about how they're made, but I don't need to see the whole process every single time. More often than not, origin stories aren't even appetizers; they're the waiter standing there with a tray of food, talking about where it came from instead of serving it to you.
If I want an origin story, I want an origin story. Batman: Year One is one of my favorite graphic novels, despite being nothing but an origin story, because it spends all 96 pages telling a compelling, self-contained tale that just happens to take place earlier in Bruce Wayne's life than we're used to seeing. The path to becoming a hero is the story, not just the first third or half of the story that takes away from the time I could be spending watching Batman be Batman.
That's why I like the first Iron Man movie as much as I do: Tony Stark is Iron Man, and there's no waiting involved to see the character you signed up for. The only difference is that he gets cooler tech as the story progresses. As the movies go on, Tony's origin story continues to play an instrumental role in his development. This is not some one-and-done explanation of how he became a superhero; the shrapnel in his chest and his fixation on building a legacy before he dies are persistent reminders of his origin story. The origin and the story are too intertwined for the former to feel like a roadblock to the latter.
That's why I also like Captain America: The First Avenger, despite it being yet another origin story (set during a time period that's been overdone in film, no less). At first, Steve Rogers is hardly the shield-slinging super soldier he goes on to become, but he's still a hero in his own right. Cap's roots as a scrawny, straight-laced, diehard patriot are essential to appreciating who this character is and what he stands for, and we don't need to wait for him to power up before he starts growing a personality or dealing with conflicts of any real consequence.
Compare this with Star Wars. (Yes, I'm about to criticize Star Wars.) Luke Skywalker lives on a boring moisture farm on a boring rock called Tatooine doing boring jobs for his boring uncle. It's abundantly clear that Luke (and the audience, if the audience is me) desperately wants something—anything—interesting to happen. When adventure finally finds him, there's a transition period where Luke is still a naive, excitable farm boy seeing the galaxy for the first time...and then he's suddenly a confident action hero, with little or no trace of his previous character traits. By the start of the next movie, nothing that happened before meeting Ben Kenobi really matters anymore. It's origin stories like this that drive me mad. Yes, it's important to Luke's character arc to show his progression from an average teenager to the savior of the galaxy, but we don't need to spend so much time with his old friends, adopted parents, and drudgerous life on a moisture farm to understand what he's leaving behind, particularly if the story never refers back to them after a certain point.
A narrative doesn't always need to develop a full backstory for the heroes, nor does it need to present all the backstory in chronological order. Super Mario Bros. for the NES drops you right into the action; there's no time wasted on playing as Mario in the real world for the first few levels so you can appreciate his humble origins as a plumber. Firefly is selective about how its characters' origin stories are conveyed, leaving much of the past shrouded in mystery until it's narratively rewarding to reveal more. In the case of origin stories, I believe that less is generally more; you can always shed more light on a character's past as a story progresses, but you can never give back time spent setting up the story people came to see.
I think the solution may be to drop the "origin story" designation altogether. Just tell one good story, instead of two separate stories that need to be told together. If we learn something about the hero's background in the process, so much the better.