I don't think the pay is fine for what the job is, but we don't know what the right pay is either because the market is so distorted by the government. (Even for private school teachers, I believe their pay gets anchored to public school teacher expectations, similar to how Medicare somewhat dictates medical pricing for the healthcare sector as a whole).

All I know is, the reason that our brightest students don't go into teaching is because the profession is low paid and low prestige. I heard that in Korea, teaching is seen as prestigious as law and medicine (with lower pay but better lifestyle), and thus you get a lot of talented people go into teaching.