Now, let's say that a hack happened some day at some exchange for about $300 million (or even $3 million, just e.g.), and the exchange immediately opens up about the hack. For a second, just think that the scammer keeps the coins in his wallet and doesn't move them for some time, however FBI and other major authorities are aware of this hack and they give orders to mixers that if a specific address is provided to the mixers (if they know exactly on which address the hacker has kept the coins), and they ask them to immediately report them about the same, then let me ask some questions:
1. Do mixers know where they're getting a deposit from?
2. If yes, will they co-operate here with the officials and let them know about the deposit?
3. If they do, how will they stop the scammer from moving his funds out of their mixer?
Firstly, hackers that are able to pull off such hacks aren't stupid, before the hacks get reported they must have already mixed the coin and transfer to other wallets then wait for the whole news to fade away before they start moving the coins or probably they would had traded them to privacy coins and held those in their wallet. But lets just say everything workout as you have said, what then stop the hackers from changing their wallet by splitting the coins between other different wallets since the previous wallets has already been identified and reported to the mixers and exchanges for them to stay on the look out for deposit from that particular address.
Unless there's some automatic means to detect any address that have interacted with the labelled address holding hacked coins then your suggestions won't be effective and the mixers can't identify were the coins are coming from. Mixer can know an address that coins are coming frim since they're centralized. Mixer can always cooperate with the government agency when they have a very strong case against them that they need their cooperation for lesser punishments although some mixers won't snitch on their customers and mixers can just freeze the account of the hackers or delay withdrawal for your last question.