The primary purposes of central banking are to privatize seigniorage[1] revenue and increase bankers' ability to control politicians. The former is achieved through the Primary Dealer system and the latter should be self-explanatory. Needless to say, since most spending is electronic transactions, the seigniorage revenue is very nearly the entire face value of the created instrument.
It's a blatantly undemocratic power grab, effectively allowing a consortium of private banks to limit Congress's power of the purse. Or at least that was the theory. As we're seeing now, that one putative upside is nonexistent and the Fed is happy to cooperate with Treasury to spend trillions a year. The rentier class appears to be consoling itself with massive asset inflation, while still banking the seigniorage.
The United States could just as easily once again fund all of its spending by creating new U.S. Notes[2] (perhaps without the public debt clause) and then control inflation by extinguishing those liabilities through taxation.