Imagine a manufacturing process, and a transformative invention that makes the product 10 or 100 times cheaper to make than any method that does not use the invention. The invention is used in-house, and there is no advantage to be gained from licencing the invention. Distributing the process to be closer to raw materials or customers conveys no advantage over centralized production. Given such a situation, the company with the invention is likely to bet they can keep it secret longer than the term of a patent.
Of course I cannot give any specific examples. They are currently secrets, or they are secrets that died with the company or died with the obsolescence of the product.
I'm having trouble thinking of something that:
1) You can benefit more from as an industrial secret than as a patented invention.
2) Society is harmed by the lack of public disclosure.