Nuclear weapons have only been used twice in war, but their continued existence has created a new dynamic between the major military powers. This nuclear standoff came to be known as "mutually assured destruction" (MAD) during the Cold War. As a result of MAD, there has not been a war between the Great Powers in Europe since the surrender of Nazi Germany on May 8, 1945, a peace that has lasted over 60 years. This is the longest period of major-power peace in Europe since before the fall of Rome 1500 years ago. The second-longest such period of peace among the European Great Powers was 43 years between the armistice that ended the Franco-Prussian War, signed on January 31, 1871, to the Austro-Hungarian declaration of war on Serbia, on July 28, 1914, which signaled the outbreak of the First World War two days later, a total of forty-three years, five months, and twenty-eight days. In effect, since November 5, 1988, every day that the European Great Powers have not been at war with each other has set a new European regional --and pretty much a world-- record for the duration of a peace.
Proposals to get rid of nuclear weapons not only threaten to upset this peacekeeping mechanism, but ignore the fact nukes are seen by more vulnerable nations as the cheapest, and most certain, way to guarantee their survival against threats from more powerful neighbors. Give a nation a choice between guaranteeing their safety with an international treaty, or some nukes, and which option will most choose?
Moreover, you can't eliminate nukes unless you eliminate the knowledge of how to produce nuclear weapons. That cannot be done, because the basic principles of nuclear weapons construction have proliferated beyond the power of anyone to destroy that knowledge. With that knowledge, any industrialized nation can quickly build nuclear weapons.
And then there are the unintended consequences. If you were to succeed in creating an international treaty that really eliminated all nukes, that would provide more incentive to create more powerful chemical and biological weapons. What many people don't want to admit is that the genie is out of the bottle, and you can't put it back.
Since no one has died from nuclear weapons in over 60 years, and you want to eliminate a weapon of mass destruction that has killed lots of people, why not go after the private automobile (which has killed millions since 1945). What have private automobiles done for peace? Nuclear power also produces power with far less pollution, and hardly any fatalities, compared to coal, gas or oil fueled plants. Despite its virtues, all things nuclear have been demonized for several generations. So it's apparently true that good deed don't go unpunished.