At its closest point, the northern boundary of Seoul lies 36 km from the DMZ. Of the Norks' tube artillery, only the handful of 180mm S-23s and a somewhat larger number of 130mm M-46s can reach that far and only then with special ammunition the Norks aren't known to have and wouldn't have in quantity even if they did. Even that would require that the guns be lined up right on the demarcation line.
The multiple launch rocket systems available to the North Koreans are similarly short on reach, and much harder to conceal in deployment.
There are hundreds of ballistic missiles but, again, their effectiveness is vastly exaggerated in media accounts. All 650 of them would have about the fire-power of a 100 plane RAF or USAAF raid in World War2, something German cities could and did shake off on a regular basis. Of course, not all the Nork missiles would be expended against Seoul, since this would leave nothing for airfields or ports elsewhere.
By concentrating their entire obsolete air force in one sector, the Norks probably can overwhelm part of the air defense system and do major damage. They could only do this once however, since it would entail the loss of most of their aircraft.
That leaves the Norks with the nuclear option, which is not specific to the Seoul area and, indeed, would probably be targeted elsewhere for strategic and media reasons.
South Korean officials know all this, whether the media do or not. They are indeed weighing the threat against tolerating an ever escalating series of North Korean outrages and extortion attempts. It doesn't balance the way the conventional pundits think, however.
(And I suspect Japan went nuke-capable - back in the Seventies when they saw us abandon South Viet Nam. This per retired S-2 types.)