It works but both CI and CO are affected by what you eat, so it’s an uninteresting factoid. It’s usually used to tell people they need to eat less and move more to the exclusion of food choice which hasn’t been very successful in long term studies.
Which is not the end all be all for diet advice, but it generally works, and at minimum points people in the right direction. Of course there are edge cases, and other important factors. Consume less and move more is what most people need to do.
Sure, but not to the exclusion of heating different things. Which I understand to be the point of the CICO hypothesis, that the type of food doesn't matter if you only care about weight loss. See the Twinkie diet for example.