I think Kim might get into Seoul, but that’s about it. The momentum peters out after that. He has no fuel reserves and an army he probably canot resupply.
One analysis I read 15-years ago suggested he might try to seize a chunk of SK territory in the mountainous area to the East of Seoul and hold it as a bargaining chip. Might be possible, but what would he trade it for?
A few notes:
Kim has a huge army. They sit alert in bunkers 24/365. If someone pushes The Big Red Button in Pyongyang, front line units are out of their bunkers and in the wire in 90 seconds. All their offensive elements, Armor, Arty, Engineers, SF, are already stationed forward.
They are an Asian Shock Army. No mess units, medical, repair, etc. Soldiers carry all their own food for 5-6 days. Holding territory is not their thing. Attack or die.
The only way we could stop them is nuc, and every prior POTUS would not do that.... but Trump might.
Kim’s big problem is what you pointed out. What does he do with it if he takes SK. All industry, supply, transport, imports and banking would instantly collapse and then Kim has another 51 million people to feed, with no assets to do so.