The most important venue for CCW reciprocity is the District of Columbia, and it’s the only one over which Congress properly exercises legislative authority.
You're exactly right, and a lot of people get caught up in the idea that they like a law, not whether the Congress has the authority. I love the idea of this law, but the Congress has no authority.
Easy legislation: "Any person permitted to carry a concealed handgun in a neighboring State, shall be authorized to carry in the District of Columbia" with the typical restrictions on carry inside federal buildings.
Immediately, anybody with a Virginia permit, or who qualifies for a non-resident permit which Virginia grants reciprocity, can own and carry in DC.
Couple that with the right to buy guns in any neighboring state, to get around DC's lack of gun stores.