Many cops lie on their police reports. How will we handle their excuses in the future, when those lies are uncovered, and they try to blame the inaccuracies on AI? It's already hard enough to get cops charged with perjury, and this just makes it even harder. But technology or not, the lack of accountability is not a problem that's likely to be solved in the near future.
In practice, many people use technology to help with writing, and there's no reason why law enforcement shouldn't do so, to some degree, as long as they are held responsible both civilly and criminally for what they produce.
That being said, are we going to actually see increased productivity in the pigs? Various research has shown that many cops arrest people disproportionately in the last hour of their shift, because they know that their department policy requires that they work overtime to finish their report, and they want the extra bucks. For cops who are gaming the system now, of course they're going to keep gaming it.