The story of Civil War sounded good but execution in the comics kind of sucked. Still, the basics work... except they couldn't work in the Marvel Cinematic Universe. For one thing, no hero has a secret identity. There will be a Daredevil by the time Cap 3 comes out, but it makes no sense that this whole thing would be over some dumb guy doing parkour in Hell's Kitchen. And the main beats simply couldn't work for a number of reasons, chief among which is that we know Cap 3 will continue the story of Cap trying to find and help Bucky.
So what we're left with here is the most bare skeletal aspect of the story: Tony and Steve disagreeing about being superheroes. They can disagree over the superhero's role in the world, over the idea of whether or not superheroes should be independent. In The Avengers pretty much all of Earth's superhumans operated under the jurisdiction of SHIELD, but by the time Age of Ultron rolls around they're privatized, being supported entirely by Tony Stark. To whom are they accountable? To whom do they answer when things go tits up? We have a police force not only to protect us but to have those protectors be regulated and answerable in case of malfeasance. Why should superheroes be any different?
That makes for an interesting kernel of an idea for Cap 3. It's also dramatically excellent in the longform MCU - the very selfish Tony Stark finally sees his responsibility to the world, while the soldier Steve Rogers realizes that power cannot be centralized under authority. This position would actually align Cap with the framers of the Constitution, who were terribly suspicious of the idea of a standing army. Done well either side can be compelling and make perfect sense to the viewer - it would be exciting to have friends walking out of the movie debating about who is right, with each having strong arguments.
It's important to realize that there is essentially no chance that a Civil War story in the MCU resembles the comic book Civil War, any more than The Avengers: Age of Ultron resembles the comic story of the same name (which takes place in an alternate dark future). The title and the barest concept of heroes at odds would be all that likely carries through, although Cap's fate could be replicated onscreen, especially as I've heard time and again that the working title of the movie is Fallen Son.
In fact it's hard to imagine how the comic storyline fits in with what we know about Cap 3, straight from the Russo Brothers - that it will continue the story of Winter Soldier and feature Crossbones. We're looking at a film that will be enormously different from its source material, except for Cap and Iron Man going head to head.
Some outlets have been claiming this film will start a Civil War storyline across the MCU, but that doesn't feel right to me. I think, like The Winter Soldier, it will have fallout that will define the MCU's next phase, but it will not be some sort of multi-part story spread over many films.
Finally, some have already wondered if the MCU is ready for this story. It definitely is. If you look at each phase as a TV season you'll see that Marvel's ending their third season with Cap 3 and Avengers 3. The stories have, in a larger emotional sense, been leading up to this:
Phase One introduced the heroes and then teamed them up as The Avengers.
Phase Two sees the heroes tested as individuals but remaining pals, as we'll see clearly in The Avengers: Age of Ultron.
Phase Three will have the heroes dealing with the final conflicts of their own stories and then being tested as a group. Their friendships will shatter, the trust will be gone. The good feelings have been established enough to make this shattering of The Avengers carry a lot of weight.
That leads to Phase Four, where the heroes will be forced to finally come together to face a threat unlike any they've ever known.
It's dark, but in the right way, coming from characters and building towards an eventual redemption. It's like The Empire Strikes Back, the beat of hopelessness that makes the eventual victory all the sweeter. What makes the Marvel Cinematic Universe great is that it's fun, but that fun must be put through the wringer every now and again otherwise you have a series of films without stakes or meaning. Your heroes have to get their asses handed to them, and it's more dramatic if they're handing themselves their own asses by making mistakes. It is simply great drama done in a longform way.
As for Spider-Man... HitFix has reported the rumor that Marvel and Sony are in talks to bring Spidey to the MCU, and his major role in the comic version of Civil War has set off speculation in a big way. I don't think this is happening, but I have learned never to underestimate Marvel Studios. Still, I'd be shocked if they shoved Spider-Man into a movie that is already pretty stuffed.
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I don't see any way Civil War could be adapted in Cap 3, it didn't make any sense when RDJ was casted in the movie and it still doesn't make any sense now.