There is another issue related, as FATF is aiming in making the crypto environment as close to the banking system as possible.
We can check the history of each wallet or block number. Imagine you became an owner of the part of the block which had been related at some point in some sort of illegal activity. In the eyes of some officials, it would make you somehow involved in an investigation related to the money laundering and your wallet can be frozen (depending on the local legislation) for months if not years. Not to mention that in some jurisdictions it can be even enough for arresting you. Even if you just eg. accepted payment in BTC for your used mobile.
Doubt that they'll be looking the "illegal activity" on a block by block basis since there is still a lot of transactions included in it. If they know how Blocks work then they know that some legit transactions that are not involved with a crime might just be coincidentally included in it, this will be more obvious if they have seen the pattern from it. Also they will see the difference in addresses used in these transactions it would be easy for them to pinpoint the affected addresses involved with the illicit activities and who they are sending it to. But if all else fails and your tx id is involved with the investigation then it is your chance to prove on where did you receive that BTC from receipts, messages, and any proof that its a legit transaction would be enough to clear your name.