Maybe the law doesn't trump it. Maybe it does. I don't know for sure. Given enough time and money, I could probably even get it to the USSC to make the decision for me. However, I'm not in a position to spend the next few years in prison and several hundred thousand dollars to test the issue. I think most of us fall in that boat.
You seem awfully concerned about infringement when you don't even exercise the right. If you believed in the power of the constitution so strongly, I would imagine that you'd carry all the time, regardless of the law. Give that a shot and let me know how it works out.
See, that's the thing about our systems. If you are really concerned about infringement, you need to partake in a little civil disobedience to get the law tested. Since I'm ok with being licensed and do carry, it's really not worth my time or money to fight a fight for someone else who would rather be unarmed than get a license. However, if you really believe licenses aren't need, take up the cause, brother! Go show them the Constitution is the supreme law of the land! Carry a concealed weapon into an airport and you can get two pesky laws shot down at once.