There were some limited travel restrictions right after the Nov 23 attack imposed by the Japanese and Philipino governments.
Unlike in some other conflict zones, a mass evacuation of the ROK could actually trigger a conflict that might otherwise be prevented. This is primarily due to the proximity of Seoul to the DMZ.
The North’s military does not have the ability to invade and hold significant portions of ROK territory like they did back during the Korean War. What they do have the ability to do (and arguably what has kept the ROK from retaliating with any meaningful force to previous DPRK provocations) is pound the snot out of Seoul with its conventional artillery and SRBMs from behing the DMZ. This is their biggest deterrent against ROK/US military action.
If the North were to detect a mass evacuation of Seoul (or so the thinking goes) they would launch a massive artillery strike on Seoul and perhaps even push across the DMZ and make some limited land grabs (Seoul lies only 35 miles south of the DMZ) under a “use it or lose it” rationale.
there have been no evacuations because all those civilians, especially the Americans are human shields and pose a trip wire that ensures the North Koreans that the US will retaliate for the civilian deaths if they attack
pulling civilians out would be interpreted by the North as an act of South Korean/US preparations for war
When such suggestions & efforts become official, it’s too late.