They are mechanical because CT is more a language than a field in its own right. They're mechanical in the same way that a lot of logic or universal algebra is—

They are mechanical because CT is more a language than a field in its own right. They're mechanical in the same way that a lot of logic or universal algebra is—the interesting stuff arises when you start making choices and using the tools to express your ideas. On the other hand, CT was invented to talk about homology, so if you want to see a ton of examples of CT being used "in its natural habitat" then look there.