Power Plant Not Main Purpose
the matrix : power plant

Why does it exist? The common belief is that it is a source of power... but strictly speaking, there's no need for simulation then, is there? In fact, many animal species... or even just a human with a lobotomy would do just fine. The screenplay makes it a little more clear. We are not the source of power, but a sparkplug for the fusion reaction. The Matrix is not about energy but control. Morpheous says as much: "What is the Matrix? Control. The Matrix is a computer generated dream world, built to keep us under control in order to change a human being into this..."

Morpheous holds up a battery. What is a battery? The storage of chemical energy waiting to be released electrically in a convient package but realize AN ENERGY DEBT IS INCURRED in creating a battery. If the machines were desperate for energy, how was the Matrix created initially? What do the Zionists run on? Clearly, there are alternative energy sources. Again, using humans isn't about electrical power, it's about something more. But the point here, is that the oft cited Thermodynamics Plot Hole is a myth. Humans aren't running the machines... fusion is.

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Evidence

1. Paradise crops. Human life is precious, otherwise the machines should still be experimenting with trying to find paradise for humanity. If you adopt the above theory that human life is not precious as a source of power then there must be something inheritly bad about the loss of human life.

2. Initial capture. At some point humanity was completely at the machines' mercy... yet they're alive. Even from a sparkplug perspective, it would have been more effecient to liquify them and use them as fuel directly than the convoluted Matrix scheme.

3. 1999. The highest point of machine and human interaction before the advent of AI. For benevolent AIs it allows them interact with humanity for evil AIs it let's them monitor and control. If the Matrix was purely a power plant, then an era without computers should have been selected... the humans with in would have been just as happy- if not happier- and have no potential at rebelling. But that risk is worth it for the interaction to the benevolent AIs.

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Objections

The most obvious objection would be Morpheous' history speech. Morpheous is often criticized for his explanation... the following analogy is used: "Saying the machines run on humans combined with fusion is like saying a 747 is powered by a rubber band assisted by jets." This is probably the wrong interpretation of what Morpheous is saying. Morpheous is not giving a scientific lecture, he's trying to convey the slavery and horror of the human condition. For example, humans can't be fed ONLY the liquified dead (thermodynamics) but are the supplemental ingredients to the mix relevant to the horror he's trying to express? No. A more correct analogy, ahem:

"Morpheous is not saying the rubber band powers the 747, he's speaking about it because it's wrapped tight around his wang. He mentions the jets in passing because he happens to be on a plane, but his immediate focus is on the rubber band, because dang if it doesn't hurt when the pilot comes and flicks it."

The other objection is that the machines are obviously evil with no other motivations. Those are addressed here and here respectively.