If we had invaded North Korea, it is highly likely that the death toll would be in the tens of millions and that several cities in Asia would no longer exist.
Add to that the fact that life expectancy around the world would probably dip sharply due to the widespread effects of radiation.
It is a known fact that North Korea has at least 6-8 nuclear weapons. It's also a know fact that China will defend North Korea if it feels the situation is not in its best interests, as they did the last time we invaded.
There are worse things than a prolonged limited regional conflict. Just because you have not experienced these within your lifetime does not mean they won't happen.