Perhaps you are not familiar with various state concealed carry laws here in America. Americans who are serious about gun ownership and will go through the effort to get the carry permit (background check required) is a law abiding citizen. Those folks also take the responsibility of gun ownership seriously. Those are exactly the people who should be allowed to be armed on an airplane, in addition to the air marshalls.
Admittedly, I only have a vague understanding of concealed gun laws in the US, but I was worried more about the risk of accidents and misjudgments--not trigger happiness--because even the most thoughtful, law-abiding person in the world can be somewhat incapacitated by, say, air sickness or what-have-you. Misjudgments happen, and I, personally, am doubtful about the general flight safety versus terrorism pay-off.
Here's a random thought, though--if an air marshall is called to spring into action on a flight, how do they usually make sure they're not mistaken for terrorists themselves? I, at least, would flip out and throw my stinky blanket into the face of anyone brandishing a gun on my plane.