I think it is wrong to call bitcoin a "private" currency.
On the contrary, imo bitcoin is much more of a public currency that any national currency is.
Bitcoin is private when it stands still in our wallets without any movements but when the first exchange or transfer happens that anonymity is slowly fading away. Government is even more involved in the tracking of the Bitcoin transaction than before and blockchain transfer data is available to all. In contrary to Monero Bitcoin is actually not that private.
Even if the government cannot control it and it is decentralized Bitcoin is more and more known and with this said its anonymity is actually deceiving. It can be traceable on the blockchain and someone with enough of the knowledge can easily track the final output of the desired transaction.