>Then where would the Harvard (and other university) students get their shirts and sweaters made?

LOL!

>And China wouldn't be able to get the US back, with just 1 or 2 warheads?

The US has in excess of 10,000, China less than 400. Given this huge imbalance in numbers and technology, I doubt any could reach the US. Who knows if any of the Chinese weapons are even ICBM's. Unlikely, since they have just learned how to put a humans into orbit. They didn't figure this out themselves, this was done via purchaseing or reverse enginering Russia technology.
http://en.wikipedia.org/wiki/List_of_countries_with_nuclear_weapons#endnote_China

>Why didn't they sort out Korea this way - a lot of Chinese soldiers pouring over the top then.

The US couldn't take the gloves off since it was the cold war and the Chinese had the support of the Soviets.