What crime needs to be identified based on transactions? Tax evasion? I can't think of any others that don't leave behind a real world mark that would be the thing that initiates investigation.

Following the money is important to investigating all sorts of crimes, as most crimes are done for money.

Arresting someone selling guns on the street doesn't stop much - they're quickly replaceable, you need to identify and determine where the guns are coming from. Same with human trafficking, drug trafficking, selling fake goods, and nearly every crime.

Money laundering is the obvious one—and the primary reason crypto’s value is as high as it is.