But look, if you have North Korean Jets making it into South Korea without our radar picking them up, you have a lot more problems than needing a STOV aircraft, like a North Korean stealth aircraft.............I mean come on, there is a such thing as planning for feasible enemy strikes and then there is completely implausible scenarios.
Look, even if a North Korean jet(which is a pretty unsophisticated piece of old Soviet technology)hits its burners(in which case I wouldn't be surprised if the plan blew apart)and flys across the DMZ, it will not be able to sustain supersonic flight for a long period of time, if at all, and as soon as it is detected F-16s out of Kunsan will be scrambled, so thats three minutes, five tops, and they are ready to shoot it down. Not only that, but it will have to evade SAM sites and AAA.
Overall, a North Korean jet getting over the DMZ, getting to Kunsan and then destroying all of the runway and taxiways(an F-16 could take off of a taxiway if nessecary, especially if you see the length of all of the taxiways and runways at Kunsan).
If I were you, I'd be more worried about a North Korean nuclear device.