Edit: that assumes that SK would be the 'liberator', but chances that it would be China are probably higher.
While they will end up killing lots of people and causing heavy economic damage the real inability to deliver on the threat that has been kept alive by those who want a stronger stance against North Korea is likely one reason they are pursuing nuclear weapons. They know they don't have a strong threat and they want one. Whether this is to truly for self protection or for aggression is for teh intelligence wonks to figure out
http://thebulletin.org/evidence-shows-iron-dome-not-working7...
Also don't forget that next after artillery fire the NK can march in couple millions of soldiers - short of nuclear strike there is no way of stopping such a mass of infantry.
Not to mention that even if N. Korea were to be "liberated", I'm not entirely sure the South would want to bear the cost of reunification. Korean reunification would make German reunification look cheap in comparison.
But for US situation with NK and SK is already good enough: no profit from invading NK, and US already profit from having military base in SK because SK pays them huge money for it.
USA gains nothing from invading NK. When any variable change and invasion will become profitable, NK will be inevitably "liberated".