South Korea should be permitted to develop economically and globally as fast as it can possibly do so. If that economic development leads to increased interaction and trade with other world superpowers, including the United States, it will only benefit South Koreans who profit from the expansive economic consequences of growth.
"The enemy of my enemy is my friend" is the old saying and as long as North Korea maintains it role as a periodic and troubling thorn in the side of the United States and all rational people of earth, South Korea will be a reliant and willing partner with the United States just like Israel today or West Germany during the Cold War.
South Korea is a valuable ally and should certainly be in America's foreign policy inner-circle. We have a long history of economic and military cooperation, including American help in the Korean War, and if we should not abandon this relationship then we should certainly also allow it to grow into something more powerful.
Given it's geopolitical location, South Korea would serve as a vital region to have strong relations with in the future for the US. With North Korea remaining a constant threat to the US, it is important that the United States is able to keep a diligent eye on the country and be as close as possible shall the tension be broken. Apart from China, South Korea is closest to North Korea. With this being said, having a firm diplomacy set between the two nations would be a very wise move for the United States. On top of this, during the recent "threats" by Kim Jong Un himself this year, South Korea has proven to be a valuable ally for the United States - This was shown through the acceptance of having the US increase their numbers on South Korean soil during the time. Furthermore, having a superpower such as the United States backing up South Korea would deter North Korea from launching any acts of aggression towards the South (pun not intended). This would be necessary in keeping any peace between the two nations.