Kudos to Coinbase- I tried sending a small amount to the account after seeing Elon Musk's tweet, and Coinbase prevented the transaction from occurring.
Moving coins between wallets is simple, it would not be possible to simply block an address to prevent cashing out.
Now I'm wondering how much BTC the attacker effectively left on the table by reusing the same wallet address, especially considering that lots of people who deal in crypto use just a handful of exchanges to send it.