Unfortunately, it's not just elected officials that are problematic for prediction markets. The Secretary of War, for instance is not an elected official nor are leaders of the armed forces and there is definitely a prediction market for war. Multiply this by every powerful appointee and every career bureaucrat and see what kind of picture that paints.
It's also low-ranking members of the armed forces that have a lot more information than you'd expect. If you just banned the high ranking members from prediction markets, I actually don't think very much would change. (There would just be slightly more delay.)
Good behavior starts at the top. It becomes a lot easier to crack down on low-level corruption if the guys at the top aren't doing it.