It won't destroy law and order because law and order will destroy (or better shutdown) the exchanges that accept that cryptocurrency first.
Physical evidence is a way to catch a criminal, as long as that evidence exists.
What if that crime was committed in the cyberspace only? Someone could not even touch or physically possess drugs or dirty dollars but still committing crime by exchanging them with that super-anonymous cryptocurrency and then in turn exchanging them with USD (= money laundering).
And I'm not talking about sacrificing democracy or freedom of speech. But these freedoms should be revoked if the line gets crossed (i.e. you act against the other people's interest). And that's when you go to jail.
First of all, government can't shut down all the exchanges, since there are decentralized exchanges, there are even the ones like Bisq that use fiat and are still decentralized. They really have no way of effectively stopping this revolution.
If physical evidence doesn't exist, then how can you be sure that crime even happened. There is a reason why I didn't count any crime that happens in cyberspace, because it isn't a crime in my opinion. You can't get killed or hurt in cyberspace. I think that cyberspace has nothing to do with the law or governments or the rest of the physical world and they shouldn't hold no authority over it. My point is that if no one gets physically hurt, it shouldn't be a crime and if they did, then there is evidence. And if law enforcement can't catch it by using that evidence, nor the evidence they obtain from cyberspace peacefully or anywhere else for that matter, as long as it is a peaceful way of obtaining information, then they shouldn't compromise other peoples privacy or peace just so they can get their job done. Biggest fish already have their ways of anonymity, as we saw in part in Panama papers, this is for the people and they just want to protect their power from the people. It is a biggest trick all regimes use, fear, to make people give them more power then they deserve. Money laundering shouldn't be a crime on it's own, it hurts no one, it is an actual crime they are laundering money from that is a problem and that should be stopped there, as other ways are unjust and ineffective. There will always be ways to easily launder money for big criminals, they are not fighting this battle so they can win or even make a dent in this crime, they are fighting it so they can hold power and have reason to exist and expand and employ more of their own people.
I think that democracy and freedom of speech should never be revoked, whatever you do, you should always be able to say your part of the story and give your opinion, as opinion never hurt anybody. It is just another way to stop people from expressing their opinion about the system, if you take away their right to vote or say how badly they were treated in the system, you can keep doing it and make up crimes for others to shut them up as well. I know you don't want to believe this is happening and it isn't happening in an enormous level at all, and is always decreasing, but it is happening. System is corrupt, everyone can see that. And in such system, even the worst criminals deserve a right to free speech,democracy and anonymity for their opinions.