Can’t be that hard to shoot down a slow rising rocket if you are firing from a ship within a few miles of the Korean Peninsula.
“Hey you little two bit monster do you think you can do this forever?”
I think if you shot it down over N. Korea, they’d be more likely to go to war, than if you shot it down hundreds of miles away.
So in the former case, you’d have the war anyway. In the latter case, since it’s less of a loss of face for N. Korea, they might not go to war. But they still might.