As you said BTC won´t make the crime worse, it will catch some dumb criminals.

I think the main problem with BTC is how threatening it is for the "old system" and they want to stop it (delay it) as much as they can. If they weren't worried about their own S they wouldn't ban/restrict BTC, they would use and explore the qualities it presents to stop crime and develop new methods to make the world a better/safer place.