The Constitution does not say this. It states that the Federal Goverment can issue and regulate money but not that it has a moneopoly. In fact, for the majority of US history private money was very common. i.e. Bank notes issued by private banks.
with predictably disastrous results:
There were significant problems with this system, in which money often wasn't worth the paper it was printed on. In theory, a bank note derived its value from its ability to be redeemed for gold or silver at the issuing bank, but what banks could live up to that promise? Those that were poorly capitalized went to great lengths to ensure that their notes weren't redeemed. For example, the Union Bank of Tennessee issued notes only redeemable in New Orleans.
In this unpredictable environment, spending a dollar required some serious thinking. A wallet might have three, five or a dozen different bank notes -- a bull's head staring back at you from a Bull's Head Bank note, or a Marine Bank bill illustrated with ships -- not to mention foreign coins from around the world and personal checks, which also circulated as money. Most bank notes traded at a discount based on the reputation of the bank and how far the note was from where it originated.
A shop owner had even more variables to consider. When a consumer opened his wallet to pay, the proprietor turned to his local edition of ''Bicknellâ(TM)s Counterfeit Detector and Bank Note Reporter,'' or to ''Van Court's Counterfeit Detector and Bank Note List.''
Thumbing through a counterfeit detector, the store owner would try to assess the value of the bank notes at hand. He took a hard look at the person handing over the bills, judging value based on the person's race, class, dress, comportment and reputation.
Counterfeiters exploited this feature of the system, and passed themselves in addition to their notes, dressing and acting as proper ladies and gentlemen. And with so many bank notes from so many banks, counterfeiters flourished. Some simply invented whole banks. Others erased the name of a failed bank and replaced it with that of a reputable one.
Of course, as 19th-century observers frequently noted, a poorly capitalized bank that printed notes it couldn't redeem was, in the end, little different from a counterfeiting operation.