The whole idea in comparison to this week's trgedy is complete garbage.
The shooter at VT had no criminal record, or anything. Yes, there were a few signs that pointed to him being a little wierd, but he was never officially diagnosed with any mental illness, so he could easily have passed the test to legally carry if it were even possible.
Were this in place, it would not have prevented this guy from carrying, and giving everyone else the ability have a gun just would have worsened the entire situation.
Sure, someone might pass a test to earn a concealed permit, and might be a model citizen otherwise, but you can never accurately predict what someone will do in the heat of the moment. Just because they're competent doesn't mean they have the metal capacity to actually diffuse a situation instead of make it worse.
Anyone could haphazardly start firing their weapon thinking they'll help the situation without any thought to the possible consequence of actually worsening the situation. A person, in self-defense, could try to shoot the suspect thinking they will diffuse the situation as a result only to introduce 1000's of other variable into the equation that could easily result in more injury or even death.
As mentioned above, you'll never stop violence by giving everyone guns just because it makes them feel like they can effectively protect themselves.
It's a bad idea.