Who wants a nuclear free world?

Not me. Nuclear weapons have kept the peace since 1945. There has been some bloodletting but never World War III. Even the Soviets were unwilling to come close to using nukes. Witness the Cuban missile crisis where the Soviets backed down rather than risk pushing the United States too hard. What's not to like?
Obama is talking up a nuclear free world. Dunno why, unless he really fails to understand world history since 1945. This deal he is pushing with the Soviets has some positive angles, both sides can reduce their arsenals and still retain enough power to turn the world into a parking lot. But promising not to use nukes defeats the primary reason for having them.
We have nukes for deterrence, in simple words to scare the bejesus out of our enemies. Promising not to use them, or not to build new models reduces the scare. Why do that? Better to have our enemies fear us than to have them love us.