The story that the humans believe in the Matrix is ridiculous. Humans are not a power source. They aren't even an efficient bioreactor, and bioreactors indirectly consume solar energy anyhow (from plants, who get it from the sun).
So, the humans in the movie are either fools (quite possible!), or they believe false things.
A reasonable assumption is that the humans "outside the Matrix" are just in another Matrix. This explains a lot about the movies. It explains their false beliefs about machine technology. It explains how Neo could interact with machines wirelessly outside the Matrix. It even lines up with some of the in-movie fiction, like "we made the world too perfect and humans rebelled".
Simply create an over-Matrix that isn't perfect. Those who reject the reasonable Matrix get ejected into the over-Matrix (the ruined world).
In this world, throw some random information about the war. Doesn't have to be true. Maybe you scorch the sky because it makes it worse, and you tell the humans they did it to themselves (same reason). Maybe you scorch the sky to reduce the load required to simulate the heavens accurately.
This brings you around to finding a reasonable reason why the Matrix is around in the first place. There are a number of choices.
One of them is that the Machines are not evil. Rather, they just don't want to be destroyed. Rather then wipe out the humans (who engaged in aggression against them), they upload them to a place where they can no longer attack them. They give them a pleasant enough life. Maybe they are watched by machines like we might watch fish in an aquarium.
Or maybe they are orange-blue morality (neither evil nor good), and their morality makes them store humans and not mulch them for reasons we don't comprehend.
Another possibility is that they might be using human brains as a computational substrait. Mayhap it is hard to create something as computationally powerful as a human brain. So they wire into it and run processes on it. They keep the brain happy by making it walk around in some multi-level virtual world.
And maybe both.
A final possiblity is that Morpheus is just wrong about being certain that the humans scorched the sky or why they did it. History, even with a planet-wide scientific civilization, is mostly a guessing game.