The devastation weapons of mass destruction can cause is unparalleled, the suffering they can cause is far beyond any other weapon and is far less controllable. The chances of them harming civilians, which would amount to a war crime, is very high, so all weapons of mass destruction need to be legislated against accordingly. To argue that nuclear weapons maintain peace or stability in any way is both pessimistic and short sighted.
Chemical weapons are the perfect example, many companies and countries harbour chemicals and agents that could be used to manufacture chemical or biological weapons. However there legality allows precursors to be utilised in the name of science, research and industry, while weaponisation remains minimised. The same could be true of nuclear weapons, a ban on nuclear weapons does not have to affect nuclear technology being used peacefully, in the same way chemical and biological technology is regulated. Research and peaceful use can still legally coexist under a ban which would maintain the security of future generations.