In my judgment the existing program is unconstitutional. As currently structured, it violates the Fourth Amendment's requirement of "reasonableness." On the other hand, it should be possible for the government to correct the deficiencies in the program in a manner that both preserves its legitimate value and substantially mitigates the risks to privacy that it currently poses.
People like to carry guns. People like to shoot guns. They will rely upon any justification they can find. But it is a canard. It has no basis in the constitution. It is a right that serves no one but the nuts with small guns who feel that carrying a weapon somehow makes them a man. This will never change.