Money is a unit of measure. It describes the relative value of things just as inches, feet, etc describe their physical attributes, except that it is a variable tied to the scarcity/abundance of the thing being measured in relation to its desirability.

A grocery coupon is a form of money, as it has a clearly defined denomination and can be redeemed for real goods, but no one would seriously consider organizing an economy around them. Getting a currency accepted widely is something best left to a currency issuing government that has the power to levy universal taxation to assure demand for the currency it can create at will.

Even those advocating for barter or Bitcoin will find themselves in need of US dollars when the tax man shows up demanding his share of their transactions. By positioning itself as the monopoly holder of the patent on US dollars the federal government is able to provision itself without producing a product or service and is never dependent upon revenue from any source.

The stock market and banks cannot create new money. They simply move money around between buyers and sellers, with banks extending that function into the future. For every transaction in the private sector there is a buyer and seller who are both satisfied with the outcome. One wishes to obtain dollars more than it wants the goods/services the other desires and the other vice versa.