Easy.
When the reigns of power flipped every few years between those who favored individual state federalism and those who favored a central unitary government, the first 2 central banks' brief lives were essentially their inevitable fates.
So, in 1913, when the party of central authority was in control, not only did they pass the Federal Reserve Act, but they passed the 17th Amendment which ended U.S. Senators being elected by State legislatures; and thus ending the U.S. Senate's role as representing the interests of the individual States.
It was absolutely no mere coincidence that both of these things happened in the same year.
