Kodak diversified into many areas. The problem is that they were always expecting the high profit margins in every product line. And they needed that due to the large R&D, worker benefits, big management, and quality control process that they tried to apply everywhere. Secondarily, they were always chasing the razor-blade model and that just doesn't work everywhere. I agree that led to some wasteful ventures like batteries and such. But in general, they preferred to sell off a company for one-time cash rather than try to operate it. For example: Carestream, Eastman chemical, Exelis, etc.
Many of these companies are able to expand in new directions. Formerly, they were constrained under the vertically-integrated structure within Kodak because they only focused on photographic products.
The good news is that many of the industries Kodak spun off are still employing people and operating in the same physical plant that Kodak built. In fact, many new food-processing operations have moved into former film-handling facilities due to the superb climate-controlled buildings that Kodak built up.
People here in Rochester have a lot of resentment that Kodak didn't pursue digital cameras sooner. But the plain fact is that there just isn't as much market to monetize even if they did beat out Sony, et al. for the camera market. Nevermind that even digital cameras have lost market to smartphones. Electronics are low-margin, especially if produced in the USA. Film was very high-margin and high-volume. If you are over 30 years old, you probably remember that using a few rolls of film a year was a big deal due to the cost. Now picture-taking is virtually free; only rarely do I pay money to print out a photo.