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That doesn't really work either. Human brains are not great at computing unless you are looking for "good enough," results, and only on some pretty narrow fields, facial/speech recognition, some physics interactions, etc. But worse than that... we're kind of using them. If they wanted us to compute, the whole function of the Matrix is just taking up run cycles. And you can't just coopt them during sleep, we need the rest periods ,or we literally die. Only one answer makes sense to me, it's a nature preserve. They didn't want to be responsible for destroying their creators, and the only other sapient species known to exist. So they build the Matrix to keep us docile. Then, the energy reclamation actually makes some sense. They're never going to be net positive, but assuming they are having difficulty keeping their society powered, they would be incentivesed to reclaim every watt of power they could from us to reduce our burden on their grid.
Humans are great computers, we're just not digital. Our brains are definitely analogue computers, where closer neurons or stronger synapse connections can mean higher voltage signals from one cell to another. This is a very powerful and nuanced form of computing. It's not great for exact calculation of numbers, but it is great for interpreting data, even extremely large data sets. Human brains (many animal brains really) are also really fantastic at image processing in particular.
If it's worthwhile to have a dedicated video card in your pc, then likewise, it would probably be worthwhile to have human brains in your evil robot hivemind. It would make some kids of processing much more efficient.
Human brains are excellent at computing certain things that are almost impossible for a regular computer. Having worked for years on computer vision I can tell you how hard it is to make computers realize simple stuff, heck, you need massive server farms just to do a basic object recognition that any 3 years old can already do. Sure, you can train a simple AI to recognize some objects, but it will never (currently) be as many objects or as precise as a person can instantly recognize.
The truth is human brains are excellent at what they evolved to do, i.e. pattern recognition. So much so that when trying to figure out data it's usually easier to plot the data in many different ways to see if something shows up. In fact usually when you try to do cluster analysis the first machine result is, let's say not great, but you can see that things are wrong and adjust the parameters.
As for your other point your brain does this automatically, they can just put a billboard with the thing they want analyzed and your brain (and millions of others) will give them the answer. Or they could use our dreams, even during sleep our brains are still active, and they could run any scenarios then. There are many other ideas, e.g. people playing videogames inside the matrix are actually controlling robots, or people working in forklifts are actually piloting construction robots in the real world, etc.
The original CPU idea was excellent, but computers weren't so ubiquitous back then, and the producers thought that the audience wouldn't understand it.
Humans solving CAPTCHA for the machines
Well, they could co-opt our brains in various ways.
That asinine stuff at an office? Maybe it's work the computers weren't good at.
Doing manual labor? Maybe it's controlling some robot doing a real world analog.
Some unskippable ad that you passively thought about? Maybe it represented work being done.
Maybe it is intruding on "spare" brainpower and if the balance glitches in some weird way? Reset you with "just a dream".
I think there's enough room for a "wetware" computing explanation. However I could see it being more than audiences were really prepared to think through. I think your "we need the humans safely out of the way of harming us, but we don't hate them and we'll keep them alive and engaged in a safe way" probably would have worked well, but they wanted the AIs to be cartoonishly bad in the first movie, and that would have been "too nice".
The best way to have it would be that there was a directive that they couldn't kill humans. Of course you need to deal with the issue of the agents taking bodies over and then getting them killed. But the matrix never made much sense in that regard anyway since neo and co killed so many innocent people it's ridiculous.