i think you are confusing fractional reserve banking with the [us] federal reserve bank
All FRB has followed the model I describe, going back to the Bank of England in 1694. The Fed is no different. The State/Crown grants monopoly power to a private cartel to issue the nation's credit and dependent currency. We're all in debt to the same cartel that uses our own money against us.
This 1943 letter by some British Nobel prize winners and various scholars and businessmen lays out the scam nicely:
...Under the world's present financial system the money, except for a now
trifling portion, is originally created by the issue of a loan at interest by the
"bankers", who lend nothing of themselves but in effect make a forced levy in
kind on the Nation by conferring on the borrower the power to purchase a
corresponding amount of wealth on the market, which wealth does not belong to
them, or those who borrow from them, but to the community. The proceeds of the
issue of new money - whether of paper or any other form of credit money -
belong to the Nation in which it is, or is accepted as, legal tender, and not to the
issuer. Herein lies the basic flaw of the existing monetary system.
Demand for Monetary Reform: 1943 letterThe scam of "I'll lend you something I don't really have so you can pretend to be rich while you're actually in debt to me" is as old as money itself. We keep falling for it.