I don't think that's a particularly novel idea, the question is how do you get people who care in an organization that has hundreds of thousands of employees (the public sector)?

You may not like the trivial answer: The same way as we do everything else. How do we get people to show up for work? How do we get people to respect data security boundaries? None of these are questions of technology. The answer is culture. We need to create a strong shared culture of caring, by hiring people that care and putting them in an environment where caring is appreciated.