The reason for that number was that: 1) you needed a number proportional to your enemies to maintain a credible the threat and show that you were "equal". Equal in this case is judged by how much overkill you posses. 2) The primary use of nuclear weapons would be to wipe out the opponents nuclear arsenal; called a counterforce strike. Which would have been made very easy if you only had a few hundred nukes. You could target 10 of your nukes to every 1 nuke the enemy had in his silo to guarantee a kill. 3) The destructive power of nuclear weapons are hyped up a bit by the media. A nuke makes a big boom, but there not that big. The largest nukes where only a few million tons of TNT, and most were much smaller being a few hundred thousand tons. Temporarily changing a portion of an ecosystem and wiping out all life on Earth are very, very different things. So it would take quite a few nuclear weapons to pummel an enemy into submission, and you need a few held in reserve "just in case."