In an earlier iteration of the script, the machines were using connected humans as a distributed computer network rather than a power source. Which makes much more sense, but apparently they deemed it too difficult a concept for audiences to grasp so we ended up with the power source thing instead.

Not only does that make more sense in the sense of “humans don’t make a great power source” (why not just use cows, or wind power, or geothermal, or nuclear?), but it also explains why the simulated world of the Matrix is so intertwined with the machine world itself, why The One is so important etc.

My head canon is that the distributed computing thing is in fact what was going on, and the humans of Zion have just gotten the wrong end of the stick.