I don't think not processing their transactions is a good move at all because one of the biggest steps done by the authorities is tracking them through the transactions they have made and simply not just blacklisting all the transactions they are seeing. I know the authorities have the power to do these but I don't think they want this to happen in the first place that's why we only see enforcement of KYC and AML procedures from happening to the Bitcoin network and also of course them knocking to all the crypto related services we have as the more coverage they have the more chances they can track down these criminals.
True, blacklisting is not anymore necessary, what the government are really doing is they monitor transactions and if you do an illegal activities, it's easier to tract the transaction as it's in the public blockchain, we have regulated gambling sites, exchanges (local and international), and other forms, if they regulate that they can impose a KYC, yes, that's what they will do so if one would cash out from illegal source of transaction, they can easily find it.
if they'll ban mixers, that would make their job easier.