I can see both sides to this. Sometimes you don't have good sleep because you're depressed and cannot get good sleep. But sometimes you can get depressed because you don't follow a healthy sleep schedule. And then you get sleep deprived and cannot cope when you get hit with stressor, thus depression ensues. The average American lifestyle (for example) is not a very healthy one. So yes people are going to be more vulnerable to stress related illnesses.

In addition, yes it can be exhausting to cook properly when very depressed. That's where things like baby carrots, apples, pre-cooked chicken strips, can come in handy. It's a start.
And fish oils are readily available.

I recommend things like these to my patients with depression and it DOES help several of them. Obviously no one treatment is going to help everyone. A combo approach can also be beneficial. Using the meds to GET things into gear and then go from there.