But by your theory, they should still be able to go to work, maintain all their relationships, and otherwise behave exactly like a non-depressed person in every way. In practice this seems very hard for depressed people and a lot of the burden of depression is effects from not being able to do this.

I think you missed my point, or I threw it by you poorly. I don't think they "should", I think they sometimes can. I sometimes can, and though I know from LW that not all minds are alike, it's safe to assume I'm also not wholly unique in my depression.

As you go on to point out, there is some baseline threshold for which people cannot will themselves out of depression or other psychological issues, just as there are weight loss diets and exercise programs they cannot succeed at.

To your analogy of the marathon: There is a right answer to whether you can run X miles in Y minutes and not physically injure yourself. I'd imagine the majority of people never come close to knowing that answer because they do not posses the ability to refrain from rationalizing themselves out of the optimal result as discomfort begins during their run. I'm aware that I'm personally really bad at this—my first .5 mile I'm telling myself I'm Usain Bolt; by mile 2 I'm coming up with manifold reasons to stop pushing. No doubt some are good and rational reasons, but others are bullshit that I need only train my mind to recognize as such in order to push through and be successful.

The answer to your second question is that their body would become upset because it's not getting the calories it needs...etc...

That's not really what I was asking. Maybe I asked poorly.

Can you instead imagine a scenario where a controlled calorie deficit was administered to a person where they received a balanced diet with all the nutrients they needed? 300 kcal was arbitrary. Pick any number. Isn't there some number that would be negligible in terms of the utility of its nutritional value and yet provide a calories deficient sufficient to lead to weight loss?

My point was that depression seems to have no such scenario. You cannot engineer a situation to "make" people be happy. Without excess food, or alcohol, you cannot get to obesity or alcohol addiction, right? Depression has no such outside variable.