Okay, I understand why military bases would frown upon radar detectors. I could go out on a limb, and I might understand why Washington DC doesn't want you to have one.
What logical purpose, does making RD's illegal in Virginia serve? It's not like they have access to good equipment, and there are enough Rabbits on the road to write plenty of tickets for. Since they are outlawed, the citizens are aware of the law, and not only can you not have a Radar Detector, you can't buy one in Virginia either. The penalty for having a Radar Detector in your car is a $100 ticket, and your Radar Detector isn't confiscated. As far as I know, you do not receive any points on your license.
Given those set of facts, I can only conclude that this is not a law designed to eliminate Radar Detection devices, but rather, a law aimed at generating revenue against citizens outside the state. Because those will be the majority of people who use RD's in Virginia.
Make it illegal to buy, distribute RD's in Virginia (where its citizens are), and give a $100 fine to anyone who has them (who will be outsiders of the state, passing through.
I'm surprised there hasn't been an attempt from a group of concerned citizens to get rid of this law.