Adding to your point, Seoul is visible from North Korea, and vice-versa, and likely has enough conventional artillery aimed at it that even without nukes an invasion would be Very Bad for the Korean people.
Another fun trivia: Seoul and Pyongyang are closer than Washington DC (Union) and Richmond VA (Confederacy) by a considerable margin.
None of that would stop the current US administration from launching a sneak attack as we've seen several times in other countries. They simply do not care about consequences.
North Korea is in such poor shape that they probably can't maintain much of the equipment much less keep the personnel trained and ready to use it effectively. Not a reason to go to war, but the threat to Soul and SK in general is likely massively overstated.
I think the strategic rational for unification completely swapped about 20 years ago. Up until the early 2000s it was likely in South Korea's, and the US's, interest to find a way to topple NK and unify the peninsula. The two populations had blood ties and common culture. Technologically the gap was growing but still reasonable. It would have been close to an east/west Germany type of situation where unification took effort but ultimately was clearly beneficial. China (and Russia) would have been losers in that unification would have brought a western friendly government even closer to their border. Additionally, NK still had a chance of re-energizing and becoming a real threat to SK.
Now however NK is in such bad shape that unification would be traumatic. South Korea would take on a problem of epic proportions, caring for and bringing a population of that size back into the broader world would be exceptionally costly and definitely not guaranteed to end well, possibly destabilizing SK in the process. Their cultures have grown apart making it hard for them to understand each other. The blood ties are not really there anymore. China and Russia would likely be the winners in that everyone sees NK as crazy and anyone helping them is hurting the world so they could get rid of that baggage. China especially would gain by having rail access to massive shipping assets to deliver goods even cheaper to the world. Finally, the US would loose a major rationale for stationing forces that close to China. They could, rightfully, say that NK isn't a threat and the massive US assets in South Korea and Japan should be drawn down.