The major military impediments to the South Korean Army marching to the Yalu are that the roads in North Korea would be clogged by civilian refugees trying to get the hell out of North Korea, and ROKA logistics capabilities in the many mountains where all the bridges would be down.
Isn't the DMZ kind of an impediment to the South Korean Army marching anywhere? It's wide. It's riddled with land mines. Razor wire topped fences and guard shacks completely block the north from the south. North Koreans who want to go to South Korea have to escape through China.