The Columbia Encyclopedia, Sixth Edition. 2001.
Bank of the United States
name for two national banks established by the U.S. Congress to serve as government fiscal agents and as depositories for federal funds; the first bank was in existence from 1791 to 1811 and the second from 1816 to 1836. 1
The First Bank
The first bank was established under the auspices of the Federalists as part of the system proposed by Alexander Hamilton to establish the new government on a sound economic basis. Congress approved a charter for the bank despite the argument that the Constitution did not give Congress power to establish a central bank and the charge that the bank was designed to favor mercantile over agrarian interests. 2
The bank had a head office in Philadelphia and branches in eight other cities. The government subscribed one fifth of the capital of $10 million, but a loan of $2 million was immediately made to the government. In addition to acting as a fiscal agent for the government, the bank conducted a general commercial business. 3
It was well managed and paid good dividends, but its conservative policies and its restraining influence on state banks, through its refusal to accept state bank notes not redeemable in specie, antagonized more exuberant business elements, especially in the West. These interests combined with agrarian opponents of the bank to defeat its rechartering, despite the support given the bank by the Madison administration. The bank concluded its affairs and repaid its shareholders. 4
Okay, you are referring to the two banks that I have known as "The First U.S. Bank" and "The Second U.S. Bank" but which I, now, acknowledge also go by the names you use.
Moving on to the more substantive issue what is it about these banks that you find appealing vis a vis the Fed.
Specifically, are you aware that these banks did not issue currency? The bank notes they did issue were theoretically redeemable in specie and were not a legally enforceable tender.(i.e., creditors were not legally bound to accept them at par in discharge of a debtor's interest or principal obligations).