It is quite easier for police whos intention is to sell the bitcoin for his own good using mixers. The traces and signs that these bitcoins are used in illegal activites will be forever forgotten.
The traces will still be there out in the dust, waiting for a proper blockchain analysis to find them out. You cannot hide the tracks of coins on BTC's blockchain, it's immutable and the records will be forever
known unlike you said.
And if it is indeed possible, of course, they can get the private key easily from the perpetrator. After that, it will depend on the court there whether the asset will be sold and entered the state treasury or will be auctioned (somehow the meaning).
I don't think they can
easily get the private keys from a criminal. It's usually either the criminals giving up their private keys for their sentence to be mild or their privkey storage was crappy. Otherwise, besides basically torturing the criminal to make him unwillingly tell where the keys are, the authorities may have no luck in finding them - or the criminal could simply say "I lost my keys".
Have just read about it and yeah it makes sense if the BTC is used for the criminals. The government really can seize it with their authorities. In this case, all the evidence can be used and seized if necessary. Moreover, if there are exact rule and regulation about it clearly.
Yeah, let's leave BTC anti-crime regulations for later (or never) - they've abused them enough.