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Nukes at the time werent that terribly powerfull and still had to be delivered by bombers. On top of that, Nuclear weapons were in small numbers and had a very low production rate.
Coupled with the fact that the Soviets and to a far lesser extent, the Chinese, werent exactly pushovers in conventional militairy strength.
And that is totaly asides from the fact that the USA didnt had any reason at all to use the Nukes. It only would've worked counter productive.