Always felt like it would've made more sense if it was using part of the peoples' brains to do their computation, as super energy efficient computers.

I believe that was in the original script, and rewritten after some exec didn't understand how brains could be computers.

If it was indeed the original script, the reason they changed to batteries is maybe not because "some exec" is an idiot, but because it worked better from a storytelling perspective.

Even if treating people as batteries doesn't make much sense as we are pretty terrible power plants, the message is clear and impactful. It is common for movies to oversimplify things, because they want to avoid having the viewer from being distracted from the main plot. It is tricky, as being too obviously wrong can breaks the immersion. I think the people = batteries analogy is a good compromise. Brains = computers, while technically more plausible would add a layer of complexity that could be a bit too much for a 2h action movie.

Matrix franchise is well known for not trying to pack in too much complexity /s

I don't think it'd have much of an effect on the story, outside of background stuff like the Animatrix, it's just an interesting little fact about why the world is the way it is. Shooting and hitting things in slo mo is still the core either way.

I'm going to bet it's simpler than that. I'm betting they changed the script for the Duracell product placement that made an acquaintance of mine a ton of money for pulling it off. Always follow the money.

https://alistentertainment.com/marsha-r-levine/