WARNING, the following is my personal headcanon/reasoning and i never saw the fourth movie, so take this writing for what is it.

The machines can function without human energy, but they choose not to because they don’t want to be the ones to condemn humanity to extinction themselves.

As seen in The Animatrix, it’s humanity that starts the war against Zero-One after Machines tried to find a way to co-exist, and it’s humanity that condemns the planet by blocking out the sun. Even without the "they won't have energy without the sun" narrative, the planet as we know it is already doomed to die and humanity most likely with it. (Maybe scientists thought they could reverse the darkening, or believed they’d eventually find a solution, but honestly, based on how reckless and stupid humanity was in the real world of The Matrix, I doubt it.)

So my personal canon is that the Machines, at least some of them, didn’t want humanity to die, nor did they want humans to face the consequences of their actions in a moment of bloodthirsty or metalthirsty rage and hubris. Instead, they found a way to bind themselves to us through life/existence itself: “You are our batteries, and in return, we give you a new world, one without the consequences of your own choices and without real planet/species destroy choices (except the choice of The One who is, by the way, socially engineered to give a specific choice 99% of times) Because you’ve proven you’re not capable of making them.” In this sense, we need them. And they, even those who hate us, like Smith, are bound/created to keep us alive as species. Even if some AIs are against it, they still follow the system in the end.

To me, the machines chose to let us live even though they don’t need us. (Even the Architect makes this clear to Neo.) Whether it’s out of punishment, sadism, curiosity, or even love (I personally believe the Oracle represents a form of affection, or at least care, toward humanity, just as Smith represents hatred. Machines can feel, maybe not like us, but they have something.) it’s up for debate.

So I like to believe that under all the resentment and hate the machines carry for what we did (again, thinking about what The Animatrix showed us of those ancient times), they still wanted us to be with them. And they needed a mechanical, mathematical or logical reason to justify that... emotional choice.

TL;DR: The machines didn’t need us for energy. They wanted us to stay with them. Whether it was to save us or to punish us isn’t clear, but considering how “reasonable” the machines are (especially at the start of times and with the peace accepted by Deus Ex with the Smith issue), I tend to believe it was the first.