In practice it's quite different. For example if you send money to a suspected terror group your bank will block the transaction and freeze the funds (that is,

In practice it's quite different. For example if you send money to a suspected terror group your bank will block the transaction and freeze the funds (that is, they don't even get you your money back), even in the absence of any crime. They won't do this for regular criminals. Even if they know that a transaction is probably related to criminal activity, the bank will just file a report and complete the transaction. Except for terrorism financing and sanctions evasion, it is entirely the job of Law Enforcement to act on reports.