Since it was confirmed that food will decay, I don't see why we can't have food that can never decay. Apiculture could also make lumberjacks more valuable. Basically we should have structures that would contain bees. In order to get them, trees should randomly, even rarely, generate a visible hive. When the tree is cut, it should fall and your health should drain to make up for the stings.
There you should pick up the hive and place it inside of the structure. Overtime, the structure should create honey and there is your supply. Fires should also be used to neutralize the bees in case you don't want to lose any health during the process of picking up a hive or taking honey from the structure.
To balance such a feature, this structure should be far from housing and areas that people commonly walk through, otherwise they will lose health.