If you know that it takes a week to acquire or harvest food and distribute it to the population, then make sure you always have a weeks worth of food in the granary. You also know that droughts and invasions are a fact of life, so plan accordingly.
As a strong independent member of the first world, I can assure you that we still rely on harvests and caravans, except caravans have been replaced with trucks and trains. The reason food in the modern world is usually only minutes away, is because there is a well-managed supply chain. Yes I can walk outside and get bananas from Ecuador, grapes from Chile, and chocolate from Belgium because the manager of my local supermarket ordered those items a few days ago from a warehouse that ordered them a week ago from suppliers that purchased them a month ago from various farmers and chocolatiers. In BattleMaster, the granary is the supermarket and the regional lord is the manager and his job is to make sure the shelves/granaries are properly stocked. If he fails to plan ahead, the food runs out and he loses his job.
Yes you are correct that the way to play is to hoard as much as possible and hope your realm runs a surplus. Now you can move on to the idea that the result of this is that everyone hates food, it is boring and offers few ways to succeed and many harsh penalties for failure.
You should also note in the first world that the interesting trade and supply chain mechanics you detail
only function when there is a vast surplus of food already.
