I think they're trying to keep inventories separate so in multi-player you can't eat (ha) someone else's supplies up. But for just single players, this would alleviate a big issue with supplies and encumbrance.
I'm legit curious because I'm not sure how long rests work in multiplayer, but doesn't the entire party still have to long rest together there? Or are long rests done on a per player basis?
If it's the former, I don't see why this would be a problem there. Either way, I don't think you could eat someone else's supplies, since it's the act of sending food items to storage/the supply chest that this entire proposal revolves around to begin with. You could still keep your food in your personal inventories or the main stash if there was any possibility of you needing to use them for other purposes.