We have nuclear stockpiles, in part, because we just can't get rid of them fast enough. At one point, the United States had 32,000 nuclear weapons. We have been working day and night to reduce that number to just under 10,000 weapons, today. However, we have and will probably always have nuclear weapons for the same reason that we have 500 pound bombs and then we have 2,000 pound bombs. It always helps to have something bigger, and it doesn't get any bigger than a nuke.
A lot of fuss has been made over nuclear weapons, but the fact is that a bombing run of two or three dozen B-52s with incendiary bombs cause just as much damage and kill just as many people as a 500 kiloton nuclear warhead. What nuclear weapons do is save the lives of pilots, the fuel need to get them there, and free up resources for other missions.
Then, of course, a lot of fuss is made about radiation. Ninety percent of a nuclear weapon's radiation is released with the first seconds of the blast. Afterward, there is a steady decline in the radioactivity, in all but ground zero, is survivable after two or three weeks and less than harmful after two or three months.
The fact is that we could use nuclear weapons, albeit on a tactical level, today and it would probably cause less combat casualties and advance the end of major conflict, if it were not for the unreasonable stigma attached to their use. This stigma, dating from the Cold War, where it was presumed that any nuclear conflict would involve all of the nuclear powers of the time, would see the use of so many weapons that they entire northern hemisphere would be destroyed. In reality, even in that scenario, it is more than likely that forty percent of the population in the northern hemisphere would survive without any significant injuries suffered due to a Cold War Era Nuclear War. Another 20 percent of the population would survive, but with limited to serious injuries suffered. That is, of course, provided that cities were ever targeted on a large scale, which some military strategists suggest would never have happened. In that case, the survival rate jumps up to eighty-five percent, IIRC.