The US military also effectively subsidizes the national defense of a large portion of the world, much of which we trade with. It's because of our treaty obligation to defend South Korea that, instead of investing in an arms race with North Korea, they can afford to manufacture cell phones and cars and televisions and trade them to us. Likewise for Japan and the NATO members.
You mean other than the problem where they have nuclear weapons (and of course S.Korea does not), are actively developing more powerful nuclear weapons?
Besides that, who needs an arms race when you have enough artillery to kill millions of people in Seoul in the first inning of a war? North Korea doesn't need to be advanced to decimate South Korea, unfortunately.