Presumably, if it gets to the point where you need a safe-haven store of value, you won't be converting it to cash. You'd be transferring it directly to the recipient in exchange for food, shelter, or weapons.
I think if you’re to the point of liquidating assets for “food, shelter, or weapons”, I would prefer a few Krugerrands that fit in my pocket. How can Bitcoin beat them in terms of durability and wide acceptance?
As others have said, Bitcoin is a very shallow market. It is "worth" a lot in principle, but good luck trying to convert it to cash.