I'll weigh in. First, it disturbs me that any of these violent fantasy characters are becoming real life mascots, symbols, or propaganda tools, of a sort, for sectors of our society. In the present, the term fake news has become ubiquitous. It is often used to dismiss anything an individual or group does not wish to accept as true or factual. Which of course means that while it is sometimes an accurate analysis, it is far more often, simply dismissive of anything that conflicts with the fantasy bubble so many now seem to prefer over reality. Embracing a fantasy character like Punisher the way people are doing, is simply more evidence of how removed from reality they have become.
Law enforcement would do far better to embrace Batman anyways. Punisher is not about justice, he is about Punishment [obligatory DUH!]. Those above the law, beyond the law, or that have subverted the law, are the ones in his cross hairs. And he isn't looking to bring them to justice, or bring justice to them; the guilty must be punished. Batman on the other hand, embodies justice. Hence, law enforcement terribly misunderstands Punisher, me thinks, or they would never use his skull.