The US has had a nationally bank since before the constitution was adopted: https://en.wikipedia.org/wiki/First_Bank_of_the_United_State.... The U.S. has had a central bank that controls inflation by performing market operations since 1811: https://en.wikipedia.org/wiki/Second_Bank_of_the_United_Stat....
The core concept of a central bank that influences the economy through its transactions with other banks has a lengthy constitutional pedigree. It predates the 20th century precedent on “independent federal agencies” by 120 years or so.
If some institution predating and then coexisting with the Constitution is enough to grant it a constitutional pedigree, there's a whole lot of other nonsense that would qualify.
More to the point, this doesn't address anything of substance from the discussion above. No one is arguing there shouldn't be a central bank, or that there's no textual/legal support for one.