I think it is a great idea but No it is not realistic and it wont work.  Who is to say that we can get every other Country to agree and start destroying their nuclear weapons and reactors yet we dont.  There is no 100% trust between each Country to actually get rid of nuclear products. 

"A lovely idea?" Lovely? What a strange word to use when referring to something like nuclear weapons. For the first time since the initial efforts of the Truman administration , a movement to eliminate nuclear weapons has developed not only from the political left but from the  center of the security elite. This promises to give the cause of arms reduction a political plausibility and importance that previous efforts, including the broad-based Nuclear Freeze Movement of the 1980s, have lacked. Whether these efforts will succeed in their ultimate goal is far from clear; but if the movement can be sustained and gather wider support, this could reduce threats of nuclear war and nuclear terrorism. There have been some excellent books written on this subject. Here’s a short list:

Arsenals of Folly: the Making of the Nuclear Race–––Richard Rhodes

The Seventh Decade: The New shape of Nuclear Danger––Jonathon Schell

Deception: Pakistan, the United States, and the Secret Trade in Nuclear Weapons––A. Levy & C. Clark

America and the Islamic Bomb: the Deadly Compromise––David Armstrong 

It’s not realistic to think that other countries will give up their nukes, and especially that radical nonstate actors — the most dangerous groups — will give up their quest for nukes.  Given that the former USSR cannot account for all of their weapons, I make the worst-case assumption that some of these groups - or at least, black-market weapons dealers - already have some in their hands.

Thank God it is not a technically easy thing to actually detonate one.