The only threat I can think of is if the fan was pointed straight at you and while you sleep as you turn and rotate the wind could be angled towards your face impeding you able to breathe in air.

That is not a threat though. A normal electric fan that you use in your house cannot impede your breathing - it is just not powerful enough.

It seems like it is something which is endorsed by the South Korean government and I'm not sure if it is supposed to be a gimmick to reduce energy use in the country.

Yes I think that was suggested as one possible source of the idea being perpetuated but I have not seen any direct evidence of it.