Mark has an article about making sure your game is Fun, he's talking about board and card games, but I think it's relevant to most games.
I understand the desire to push the player towards confrontation with the final boss. I don't think Food is the right tool for that goal.
The scarcity of food doesn't make sense. If food was that scarce, all the people would have starved to death. Real world people can go days to weeks without food, in game you're lucky to last a day.
If food is not the right tool for that goal, why? Your stated reason is nonsensical - the player character is an adventurer, venturing into frontier and wilderness territories all alone - of course starvation is a possibility. The player character is going a long time without food, as you're not actually carrying fifty Food with you; as an example, resting at the inn recovers a large amount of food because you eat a hearty meal, because the food stat itself is more of a satiety stat. Same goes for sharing a meal with Urka or Trudy.
If we wanted to be strictly "realistic", then the first time you were severely injured in battle, you would die of sepsis, and even if you survived, it would be with debilitating injuries that would at best put you out of adventuring for months, and at worst end your career outright.
