That was why Hamilton’s conception of a National Bank was to be privately owned and run.
However, a form of fractional reserve banking has been in existence since the first banks were formed.
A privately owned central bank is no better. It takes away all the checks and balances in free banking that keeps banks (even with fractional reserve banking) from over inflating (or inflating at all). Fractional Reserve Banking has been around since the moment bankers realized people didn’t come in to collect their gold: they issued fraudulent receipts for gold they didn’t have. The problem is government allowed this practice to continue and actively encouraged it.