Removing humans from the information loop can have catastrophic consequences. I recommend reading this article about how human intervention prevented a nuclear war. A computer would have fired the missiles....
But the reason there was an incident at all was BECAUSE of a human error. The commanding officer (the Major) allegedly issued the nuclear strike codes by mistake. He was later court-martialed, according to the article.
Also, a computer probably would have summarily rejected the mistaken launch order because it did not conform to requirements (i.e., not being in DEFCON-1).
On the other hand, a different human being that night might have launched the nukes as instructed, without checking all the prerequisites.