The purpose of a fatigue system is to make all classes want to rest.
Systems where only spellcasters need to rest are weird to begin with. Imagine multiplayer where the mages are nagging to rest but the fighters who don't need it are just ignoring it. All classes need an incentive to rest. Fighters and Rogues will want to rest when they have a -4 fatigue penalty to attacks and saves.
I think instead of a gold tax, it could consume food? There are a lot of food items but it still would act as a resource being consumed?
I really don't want to micromanage apples, melons and pigs heads. I want the food stuff and other trash loot out of my inventories. Other RPG's don't make you deal with pointless trash like this. Still this would be a better use for the food items than having them double as healing potions. But what if you run out of apples? Do you have to backtrack all the way back to Druid's Grove to buy more before you can rest? If all food was consolidated into one item such as "Camping Supplies" it would be much easier to keep track of available rests.
If long resting doesn't cost you anything, there's no incentive to not rest after every fight and no reward for managing your resources efficiently.