Should concealed carry permits be required to carry firearms concealed?

In the United States today, most states have "shall-issue" concealed carry laws, whereby the sheriff of a county must issue a concealed carry permit to anyone who meets the requirements. Those requirements usually include no history of criminal activity, no history of mental illness, and some training. However, two states permit "constitutional carry," meaning that any law-abiding citizen has a right to carry a concealed firearm, without the need for a permit. Is requiring a "concealed carry" permit a violation of the right to self-defense? Or is "constitutional carry" a dangerous form of anarchy?