One example I can come up with now - image classification / segmentation / regression problems.

Unfortunately, not all data is available or provided in a data "friendly" format - sometimes all you get are image files, and similar. Maybe you want to read some value off these images, count objects, or whatever - which traditionally has been done by trained/skilled workers.

With CNNs, it _can_ be a trivial task implement models for solving the above problems. That's time and money saved for a business.