> Try not eating for three days when you're otherwise healthy, and observe what it does to your body and mind.
That's the point here. It doesn't do anything to your body and mind. Both will continue functioning at the same level as before. Three days is not a significant period of time to go without food. This is like asking what happens to your car if you drive it for an hour without refueling. Nothing will happen unless it was already running on empty.
There is a very common belief that missing meals for a single-digit number of days will hurt you, but this is not based on reality.
Note that, if you assume that fasting has negative effects on your body and mind, the immediate implication is that eating is more important when you're sick (and need to be functioning well), not less important. The implication is false over the short-to-medium term, and this is possible because the premise is false.
I've been in a situation like this three times (twice in my youth and once about a year ago). Five days without any food, only water and herbal tea.
Only the first 18 hours or so are a problem (depending on your eating habits) day 3-5 are the best, because your mind is really clean and you don't feel any usual discomforts from eating late or eating something you shouldn't.
You do feel light and weak of course and I'd recommed avoding any hard work but otherwise 3-5 days without food is completely fine (assuming you don't have any conditions that require a stable intake of food).
Try not eating for three days when you're otherwise healthy, and observe what it does to your body and mind.