the technology is not private, but the coin ownership is. As there is no government institution that can print/create coins and use that as to control inflation, adjust for GDP etc. and set rules on how the newly create money should be used. This leaves supply of coins in the market to people or private institutions that have a lot of them and thus money supply is privatised.
And yes banks are private but the money supply is ultimately controlled by the Fed and thus the democratic system is responsible for the money supplies as it appoints the governing body.
the p2p network is free to all, just like handing cash money is free to all.
Individual freedom is not the same thing as democracy, to much individual freedom is ultimately anti democratic. Because this will always favour the rich and powerful.
The monetary system in many places was already mostly private, most money is created by commercial banks and we have institutions like central banks with private ownership in many countries.