I've always been surprised by questions like this. Why is (say) gold valuable? The gold supply fluctuates unpredictably depending on gold strikes and without any consideration for creation of underlying economic value (so is inherently inflationary, except for gold strikes). The big gold strikes of the 19th century were each associated with economic boom/bust. But the underlying utility of gold is low.
Some people complain about a central bank "controlling" the money supply (let's not forget that you "create" money when you use your credit card and "destroy" it when you pay your bill), so monopoly there. That's a fiat too.
In terms of value, the shilling case makes more sense if you think of money in its role of signalling (there are lots of bananas available right now so the price is going down -- don't bother to go harvest some more until the price goes up) rather than as a store of value. That's why people don't worry about counterfeits. Presumably the actual measure of wealth there is not monetary -- perhaps land, more likely some kind of family/community strength.
As robots drive the marginal price of goods and services very low and humans live on UBI, the signalling role will become more significant than the wealth role.