I'm assuming you're in NYS? Can't help you. Anywhere else something so stupidly silly wouldn't be an issue. For Christ's sake, back in Mlps MN they elected a US Congressman who had over 600 unpaid tickets including several for DAS. Good luck.
I agree to a degree that traffic infractions alone are a silly reason to deny a permit. However, one has to consider the history, frequency and. If a person has proven themselves to be a danger to society with a vehicle, why would we want to give them another lethal weapon to be irresponsible with?
I'm not trying to start a debate on the topic, just pointing out what is likely the reasoning behind the thinking. And that's assuming that a history of license suspensions, reckless driving and/or speeding will have any impact on whether or not they issue a permit. (Not referring to the OP, here, just talking in general).
As to public figures, well we have you beat. Forget traffic tickets! In New York City, it is impossible to get a pistol permit - they have different and more restrictive laws than the entire state.
Still, where average Joe cannot get a permit to own a handgun, Imus (the radio personality) apparently has a CARRY permit! I don't know about his driving record, but he has a history of drug and alcohol abuse. I also recall some violent behavior that made the news over the years. So a nasty drug addict, alcoholic gets a CCW in the city where Joe Clean Cut will likely get denied the ability to simply keep a pistol in his own home.
Politicians, celebrities and other public figures don't live by the same rules as the rest of us.