Regarding North Korea---
They arent a threat to us. At best...they might have a theoretical ability to launch one missile that might make to the US west coast with a nuclear warhead that might detonate.
We, on the otherhand, almost certainly have at least one Ohio-class ballistic missile submarine stationed off of their coastline at all times. Each Ohio boat has 24 Trident missiles that can carry up to 5 nuclear warheads. Our ability to lay waste to the entire nation of North Korea within minutes is actual, not theoretical.
Kim Jong knows this. He may be crazy but he isnt stupid. He doesnt want to get nuked. He's going to make a lot of noise and empty threats, but that is it.
Ideally we would withdraw our troops off of the Korean penninsula entirely, but the problem with that is that South Korea and Japan are both signatory to the nuclear Non Proliferation treaty and have pledged not to develop nuclear weapons. They are both face to face with an adversary that does have nuclear weapons, so if we do not agree to help defend them against that threat they may very well be forced to build nukes of their own. Our presence there gives those nations protection under our "nuclear umbrella" that they would otherwise have to develop themselves.