Shooting down drones, especially high flying ones with out endangering civilian property is not easy, but it is also not impossible:

President Yoon Suk-yeol on Tuesday criticized the military’s response to North Korean drones that intruded across the inter-Korean border the previous day, saying the incident exposed some problems with South Korea’s readiness.
Korea Times
Speaking at a Cabinet meeting, Yoon said the military should be better prepared for such intrusions by North Korean drones and vowed to create a military unit specializing in unmanned aerial vehicles as part of efforts to strengthen South Korea’s air defense capabilities.
“We have a plan to create a military drone unit tasked with monitoring key military facilities in North Korea. But we’ll expedite the process of creating the drone unit after the incident yesterday,” he said. “We’ll also introduce state-of-the art stealth drones to strengthen our surveillance capability.”
Yoon also voiced regret over the National Assembly’s decision to cut the military budget for anti-drone operations, saying the incident once again showed how dangerous it is to rely on North Korea’s “good faith” and paper agreements for peace.
You can read more at the link, but it is amazing that funding for anti-drone operations was cut by the National Assembly. Drones is obviously the future of warfare. Their importance can be seen right now in the war in Ukraine. This incident should give President Yoon all the rationale he needs to pour money into the new drone command he wants to establish.