If the currency is acquired through mining, then it doesn't have to flow through an establishment that has a financial license. It can still be traced, but identifying the individual is much more difficult.
And there are other ways to make things hard to trace. Buy for cash on localbitcoins. Go via a privacy coin. Go via a sketchy exchange.
Miners still have to record the BTC they've added to the blockchain if am not mistaken.
The miner reward is sent to a bitcoin address. Anyone can create a bitcoin address without going through any 3rd party so it’s totally anonymous until you spend it.
Okay. So basically useless. And not exactly anonymous since to use it in any way would ultimately defeat the purpose.