This is wrong. I used to believe this too, before I lived in South Korea. I have talked to U.S. soldiers in SK about this issue. They told me the US remained here to keep South Korea from invading/bombing the North when they provoke the South, which NK is fond of doing from time to time. See here and here as examples. Before they had nukes, North Korea basically admitted that if a war occurred they would do as much artillery damage to Seoul as they could since that is basically all they could do in a conventional conflict. With nukes the best they could do would be mutually assured destruction.
North Korea has little fuel and outdated military equipment. They have troubles even meeting the basic needs of their citizens. They have pretty much zero surpluses of anything. They have a large army, put how well did that serve Iraq (5th largest army in the world at the time) when they faced a modernized army and Iraq had enough fuel for their vehicles. South Korea has a modern military. They are one of the 10 biggest military spenders in the world. They can defend themselves. If we leave they will quickly develop their own nukes. Followed by Japan doing so as well.
We remain to try to keep things on an even keel, or at least we did before Trump. NK currently would get crushed in a conventional war with South Korea. It is not 1950 where the North had all the industry. Nukes are a way to ensure NK's survival long-term, as even though they would lose any conflict, they could cause large scale damage to many countries which the US and it's allies would want to avoid (if NK can get their rockets to work correctly). NK won't give them up easily. The unsaid reason we want NK to drop their program is to keep Asia from a nuclear arms race. If they don't disarm, South Korea and Japan will quickly develop their own. Politicians in both countries are starting to call for their development. This is why China would prefer NK disarm as well. If they don't, China will gain two more countries with nukes on their doorstep.