It doesn't make any sense, of course, because it's a movie.
But hey...if we're going to extrapolate wildly from sci-fi, let's at least know what the stories said.
Ironically, if you ask Google, the Gemini Annoyance AI [1] confidently asserts that what you're saying is true, but if you follow the links they give, none of them support the claim, and the further you click, the more it becomes people repeating each other's speculation and hearsay and calling it evidence. For example:
https://scifi.stackexchange.com/questions/19817/was-executiv...
Typical internet story.
[1] Aside: I am far more worried about the influence of AI gaslighting on mushy-brained humans than I am on AI destroying the human race. The dystopic future of AI is people.
https://www.reddit.com/r/matrix/comments/1qatv42/is_it_your_...
There is some stuff online suggesting that the original script had that angle, but the movies did not, and AFAICT it's fanfic.
We should definitely use this stuff to guide our thinking about the real world, though, and not, say, Asimov (or a million other science fiction authors), who had an optimistic version of the same thing. Those are wrong.
Whereas using our brains for compute (in the background, or during REM sleep) makes perfect sense; power efficiency is excellent.
People obviously know this stuff is absurd on some level, but it doesn't stop them from cherry-picking the parts they "like" (i.e. fear) and ignoring the rest.
What's your N(doom)?!
Everyone panic and give me money!
There are other sci fi stories which use humans for distributed computing and they don’t realize, but I don’t want to spoil by naming as it’s something of a revelation.
(I do realize the Matrix is a fantastic movie, but entertain the thought? At any rate, the idea that robots only run on solar and wouldn’t just use nuclear is far more stupid.)
It's a movie based on a war with machines. Like if Skynet won but didn't actually want to kill all the humans. In fact, in the tv show Sarah Conner Chronicles, a liquid metal T1000 goes rogue and decides the only way forward is to find a way to coexist.
Pick up an Asimov book in the Robot series, or any number of novels written by lesser authors in the 1950s. Fiction reflects broader societal anxieties.