Can Apple do a better job at solving crimes than the FBI

Anecdotal evidence of government incompetence is not the issue. Rather, why doesn't Apple sue the govt for negligence in preventing terrorism in the US. AND simultaneously demonstrate they are better at solving crimes than legacy methods. Is it possible to solve crime without violating privacy? Since clues are largely historical data in the private user space, the traditional approach is difficult. Rather, the question is whether there is enough data in the public user space to identify crimes and to tag the individuals committing them. Perhaps all crime data should be public? (Wasn't it once this way in early America?) After all isn't the best way to prevent future rule breaking to reveal and illustrate and explain current rule breaking?

Can this problem be modeled with a small example?