A nuclear weapon can be used as an Electromagnetic Pulse if detonated high in the atmosphere. When a nuclear weapon is detonated that high in the atmosphere there is no fallout, no soot produce to cause a nuclear winter, and no nitric oxides produce to weaken the ozone. Plus use of a nuclear weapon to produce an EMP produces few casualties, while some would die because of vehicle accidents and lack of electricity, it would over all kill fewer people than conventional weapon would require for the same effect.
Nuclear weapons are the produce the largest explosion of all current weapons making them some of the best options to intercept a large number of ballistic missiles close together. While alternatives are cheaper for taking out single ballistic missiles, nuclear weapons are the best for taking out a volley or another nuke using counter measures. The shear fact that nukes are the best counter for massive amounts of ballistic missiles is a good enough reason to keep them.
Low yield airburst nuclear weapons can be used to take out hardened missile silos. While conventional weapons have some capabilities to take out enemy ballistic missile silos, they don't have as high of probability of success as a single accurate nuclear blast. It is important to note that air bursting nuclear weapons produce little nuclear fallout and little nitric oxide. Also important to note is that low yield nuclear weapons produce less intense flash meaning they are significantly less likely to produce a firestorm and thus would not produce a nuclear winter. On top of that, enemy missile silos aren't filled with much flammable matter as a city thus producing no soot.
Nuclear weapons can also be used to destroy incoming meteors and asteroids. It is important to know that meteors and asteroids can do several times more damage than any nuclear weapon can. Giving up the strongest thing we have against these forces of destruction seem like a bad idea. I much rather have a nuclear weapon and not need it than need a nuclear weapon and not have it.
The semi/non lethal uses of nuclear weapons are not enough reason to not abolish them. This is because of a variety of reasons. While I do agree that there are some good points in regards to keeping nuclear weapons, there are still many dangers associated with them regardless of whether they are lethal or not.
One of the major dangers of any nuclear substance is that of radiation. Radiation is a massive danger if in high levels. It can damage and contaminate the environment, damage and destroy the ecosystems of different animals and organisms, negatively affect the health of those who construct, use and are around the weapon, as well as the fallout from use of these weapons can be catastrophic as seen throughout history, especially when they are used for a lethal purpose.
A nuclear weapon is only non-lethal if the intent of those using it is non-lethal. Such weapons can and have been stolen. Even if they were originally meant for a non-lethal use they can be used to create a lot of damage by the groups who stole it (if it was to be stolen). Even with the best security, such a risk of theft cannot be entirely eliminated, and even if such groups did not steal a nuclear weapon, they could still target the areas these weapons are held to cause a lot of devastating fallout.
There is also the risk of the manufacturing process of these weapons going wrong and causing a negative fallout as well, especially in regards to radiation. Many nuclear power plants over the years have malfunctioned and as such released radiation into the environment and ecosystems around it. The thing is that these power plants wouldn't have been used for a lethal purpose, and neither would the areas of which nuclear weapons would be manufactured.
These places also bring up the problem of toxic nuclear waste that lasts for thousands of years and again can be used by terrorists and other such groups for a lethal purpose.
On the point of nuclear power plants and the manufacturing sites for such weapons, they (like the storage places, etc. of nuclear weapons) again provide a potential high risk target for terrorists and the likes that, if attacked, could have a devastating fallout.
Then there is the argument of the lethal use of nuclear weapons and the questioning of the morality of such use.
And there is one last problem - many sources of radioactive material used in nuclear weapons (such as uranium) are finite resources meaning that they will not last forever and cannot be easily replenished over a short period of time.
I am not saying that nuclear weapons need to be abolished (although I do think we could do without them), but that more reasons than the statement above needs to be given to not have them abolished. There are too many risks that need to be countered for nuclear weapons to just not be abolished due to one single reason.