Is and ought be. There are various different experiences and several schools of thought on that subject in US history. An early pair were Hamilton and Jefferson. Both were familiar with the example of The Bank of England. Hamilton got a similar privately owned bank, The First Bank of the United States:

The First Bank of the United States was a national bank, chartered for a term of twenty years, by the United States Congress on February 25, 1791. Establishment of the Bank was included in a three-part expansion of federal fiscal and monetary power (along with a federal mint and excise taxes) championed by Alexander Hamilton, first Secretary of the Treasury. Hamilton believed a central bank was necessary to stabilize and improve the nation's credit, and to improve handling of the financial business of the United States government under the newly enacted Constitution.

Officially proposed to the first session of the First Congress in 1790, Hamilton's Bank faced widespread resistance from opponents of increased federal power. Secretary of State Thomas Jefferson and James Madison led the opposition, which claimed that the bank was unconstitutional, and that it benefited merchants and investors at the expense of the majority of the population.

Both Jefferson and Hamilton turned out to be right in many of their assertions about the bank. The charter for the First Bank of the United States was allowed to expire in 1811. The Second Bank of the United States was chartered by Congress in 1817, famously opposed by President Andrew Jackson, saw its charter expire in 1836, becoming a private bank, and was liqudated in 1841. Over its term it demonstrated both the benefits and the risks arising from a national bank.

There was no other national bank until the Federal Reserve System was created and came into effect on December 23, 1913. However  United States Notes were issued directly by the US Treasury from 1862 until 1971. Initially, these Notes were fiat money, legal tender by law and not convertible to gold. After the Civil War banking interests convinced Congress and much of the population that convertibility should be restored. Doing so arguably led to The Long Depression, 1873-1879 and the enrichment of some of the largest banks in the USA. As the population of the USA was still heavily agrarian and only partly dependent on the market economy, The Long Depression was felt less acutely than was The Great Depression of the 1930s.  

As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."

The regulation of interstate commerce clause implies the power to regulate the payments systems used between states. That is, Reserve Notes, and Treasury Notes (greenbacks) before them, operate under the legal force of an act of Congress declaring them to be legal tender in settlement of debts both public and private. A state power to over-ride that would be a state power to discriminate in favor of in-state debtors and against out-of-state debtors, and so would be a regulation of interstate commerce, which is a power reserved to the Federal government.

A state could accept anything they want to accept, but they cannot refuse to permit the acceptance of Federal currency.

Federal restrictions on local money systems have normally been under a later layer, the power to tax incomes (16th: Income Tax, 1913), wherein income received in a local currency must still be declared and income tax paid on it as if it had been received in Federal currency. "The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several states, and without regard to any census or enumeration."

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.