In my mind something like this proposal is essential for a survival game.
My idea for implementing is somewhat different. Every food item should have a value for protein, carbohydrates and vitamins/minerals representing the % of daily requirement they provide. Over eating protein and carbs build up a fat deposit that can be used when there is a shortage, excess vits/mins are flushed out of the body and not stored you need some most days but only a relatively small amount is needed. Extra food sources may be required like collecting offal from carcass' and fruit or nut collection from some trees, pine tree seeds are really good sources and taste good to.
Lack of enough food, as now, leads to starvation penalties and lack of vits/mins leads to sickness (injury) penalties.