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.
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.
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.