You can keep the btc private, You can mine to a virgin btc address via nicehash.

And as long as you do not cash it in it is private.

If you want cash for it and privacy along with that good luck. I would argue that if that were possible the governments of the world would end it.

The do not mind that it can be moved from address to address around the world. They do mind if you convert it to cash on the sneak.

I would argue it was never design for that.