What are the use-cases, and when would such a policy have led to a drastically different outcome (in the case of a crime being committed, industrial espionage,

What are the use-cases, and when would such a policy have led to a drastically different outcome (in the case of a crime being committed, industrial espionage, or what-have-you)? If I have a laptop encrypted with luks or whatever, then what? What are the consequences of non-compliance?