Full disclosure: I knew several city policeman, and a few county sheriffs, which I why I tend to have a not very favorable opinion of law enforcement officers. Yes, a small number, but it does tend to color a person's opinion of LEO's.
I don't think that a trooper should be fired for speeding a little over, but I do think they need to realize that they are not above the law. All the LEO's I knew tended to believe that they deserved to be treated more leniently than a civilian. I've passed a few state troopers that were running about 2 mph under the speed limit on the interstate, and had a whole line of cars behind them. I just waved as I went by. They just smiled and waved back. :)
Not all LEO's are bad people, far from it. But the job beckons to a certain type of mindset, and those are the ones who need to be weeded out. Like Douglass Adams said about something similar to that: “Anyone who is capable of getting themselves made President should on no account be allowed to do the job.”