It's pretty high on the anecdotal evidence and low on actual stats, but it feels true to me. I've been in Korea almost 10 years and it really is much harder to get a job these days in Korea than it was back in the old days.
It's still possible to get a hagwon job easily enough but they seem to be getting pickier and pickier about things like gender (females), country (North Americans) and skin color (white). Public schools are cutting Native English speaker positions left and right, especially at middle and high schools. Universities have upped their requirements such that even someone with a masters degree and a couple years experience at a public school or hagwon in Korea can find it quite difficult to get their first uni job.
Maybe Japan is the answer?