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If they just stop committing crimes, then there's no fancy press release saying how great the DA is or whatever.That's an interesting observation on how people respond to their incentives.
If I'm a DA, my job description is probably not to reduce crime. It is to successfully prosecute crimes that have already been committed.
Of course, as a thoughtful and honorable person, I will naturally want to see if I can also reduce crime, not just prosecute it. But that is not the direct incentive I'm given.
As a software developer on various mid-size teams, I've often found that I don't get much of a boost in my performance reviews when I find a way to make the entire team more productive, e.g. by solving a nagging problem that is affecting everyone.
Instead, I get more highly rated by just making sure I knock out all of my own Jira tickets for the current sprint, and ignore those more global problems.