Dnd is a game too afterall so you dont need to expect everything to make sense..but yes you can officially stuff some food in your mouth as a free action.
What page has the total healing per food eaten? All I can find is its relation to exhaustion...
All those less necessary stuff is usually in GM guide, I remember a part for drinks not sure about the food. So its at DM's discression as usual I suppose.
See now this is what I thought, but what does free in combat healing do?
It ruins the balance of healing spells.
Like there are consequences to all of these choices. Eating should not heal in combat.