I’m an actual engineer with a degree and everything, although this is not my area of expertise, it’s one I’m familiar with.

They could do something like you suggest, but every step becomes more expensive and less effective. The exhaust from a coal fired power plant is still plenty hot, and more energy could be extracted from it. But it requires more and more to make less and less.

The curse of every engineer is to see a way to them every waste stream into a useful product, but not being able to do so profitably. (Which means no-one will approve the project)