cargo shop parked 12 miles off shore can easily hold a lead cased nuke. the Navy does not stop and search them all.
Any anti missile systems could not respond fast enough to stop a missile launch from such a ship before it covered several miles. A simple time problem. Even if it detonated 12 miles off shore, the fallout would end DC as a viable place to exist.
They’ve thought of that, especially about missiles launches from ships, so they significantly extended the inspection zone for the Coast Guard. I believe it is now 200 miles from the coast.