The Constitution says they don't. The US government only has the powers explicitly granted to it in the Constitution. Creating a central bank isn't one of those powers.

It's pretty far-fetched to argue that any person, historical or otherwise, has more claim to authority over federal powers than the Constitution. Who are you to argue against Article I Section 8 and the 10th Amendment? And the 9th for that matter?

commerce clause gives congress the power to set up a central bank. also

> To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;

regulate the value thereof literally describes a central bank.

"Central banking" is an excessively broad interpretation of regulating commerce between the several states. Further, delegation of enumerated powers is not itself an enumerated power. Just these two interpretations alone are enough to give the federal government near limitless economic intervention power, which it is blindingly obvious the Constitution's authors did not favor (see their extensive writings and the Preamble to the Bill of Rights).