I can understand the concern with a "DC Movie-verse" that once you've poured cream into your coffee you can't unmix them, but in this case I don't think that's really that big of an issue. If you had Superman and Captain Marvel in the same world I could definitely see where problems would start, since you'd more or less have two Supermen sharing the same world, but each of the Big Five have pretty distinct motivations and skill sets that keep them separate outside of the Justice League just as much as their geographical locations do.
Superman: He has super-human strength, can fly, is bullet-proof, can shoot heat blasts from his eyes, has powerful, icy breath, is fast, and has X-ray vision. He's the most powerful of DC's heroes, but the challenges that he deals with are usually physical in nature, whether it's fighting a super-powered monster or shoving an asteroid away from the earth.
Batman: Has super intelligence, is a master martial artist, can make himself virtually invisible with his stealth training, has a wide array of gadgets and technology that he can use to fight his enemies and solve crimes. His challenges are usually mysteries that put himself an others in physical danger. He's a detective who can beat the crap out of most non-powered foes. If there's a madman with his finger on a red button, or Batman is the one who can stop them.
Wonder Woman: A highly trained Amazonian demigodess who has immense physical strength and agility. She is not as strong as Superman nor is she as invulnerable, however she can still throw cars and block bullets with ease. She is also better able to defend herself against supernatural energy than Superman, since her armor is was made by the Olympians. She knows how to use just about any weapon, she has the lasso of truth, and she is an excellent negiotiator. Her challenges deal largely with ending conflicts and finding the truth, preferably by peaceful means but by force when necessary.
The Green Lantern: Has a super-powered ring that can create constructs out of solid light from his imagination, as well as flight and sustenance in space. He is more or less a space-faring beat cop who hunts down galactic criminals who fall under his jurisdiction. He's a powerful member of the League, however he spends much of his time in space.
Flash: Can run much faster than Superman (under enough stress he can run faster than light), has split-second reflexes, and is physically athletic. His challenges usually involve him beating a clock or defeating something that is as fast as he is, which is usually faster than what any other superhero can deal with.
While there is some overlap between the various heroes' hypothetical "turf," for the sake of the movies it's pretty negligible. As for questions like "if Batman exists in the same world as Flash, why didn't they have Flash rescue Harvey Dent and Rachel Dawes?", first of all, we can assume that like the animated DC universe, Batman was the first costumed hero in this world. Second of all, the Flash cannot be everywhere at the same time, even if he is the fastest man alive. No superhero is aware of everything happening in the world at all times, and that's why they usually stay in one city.
When they heroes do fight a global crisis, it's usually one that only they can stop. If there's a secret plot to destroy the earth, Superman probably won't know about it, but Batman will. Batman may not know how to end a war, but Wonder Woman does. Wonder Woman may not be powerful enough to stop a meteor from hitting the earth, but Superman is. When there's a crisis that none of them would be able to solve on their own, that's when we need a Justice League, and that's what the movie's focus should be. The reason why DC's Big Five are the Big Five, is because they are DC's most iconic characters who have the least amount of redundancy.