How did communism win in both China and Korea if the US had nuclear weapons?

china is close to Russia which was the birth place of the form of government that eventually collapsed on itself, and so we Korea.  Now moving on to why the US failed to stop the spreading of communism, the use of nuclear weapons was unnecessarily devastating to the country and the aftermath of the detonation of a nuclear warhead would leave the land uninhabitable from the radiation.  And for using a nuclear weapon in war without needing to, the relations between every other country in the world would worsen with the united states (It's hard to know how the world would react to it but it wouldn't be positively).  For a short story: using nuclear weapons as a regular payload should and must be refrained from usage as much as possible.

Explanation:

not to sure sdi, strategic defense initiative

this statement is   true