This system is not internal to US. Most countries have more or less independent federal bank and similar system.
>Whatever money may be, ultimately, it is supposed to act as a store of value for your labor, ingenuity and good fortune.
This is outdated idea and source of much confusion. Yes, money should act as reasonable store of value in short term. Money should not have store of value property that is better than alternatives. It should never be good investment. Money should be the most liquid asset, unit of account and medium of exchange before being long time store of value. Because contracts (including wages) are defied using money as unit of account, small inflation forces constant renegotiation of contracts. It's fluid in the gears of the economy. Store your value elsewhere. It's easy.
Money is just an asset. Theoretically, you can define money as the most liquid asset. Transition from money to other assets is fluid (different M's) based on them being money-like and there is nothing confusing in it unless you falsely assume that money should have some kind of magic substance that other assets don't have. Your car can be more money-like if you turn it into financial instrument by taking a loan against it.