Toby Ord's precipice alert hits everybody, not just the hero and villain in their final thrilling cliff edge encounter. There are still good reasons for focusing on nuclear weapons, even though they have been around for 78 years and counting.
1. Biological and chemical weapons are banned under the 1972 and 1993 Conventions which most states - Assad excepted - observe. 2. The challenges of climate change and disease are massive, but more speculative and require long term measures. (The big problem with democracy is getting attention past the next election.) Nuclear weapons can turn threatening in minutes. 3. The full impact of technology in general has yet to be digested by moral thought.
I don't see us getting over the 15 minute nuclear alert syndrome by legal means only. It has been much more difficult to put nuclear weapons into the box than their biological or chemical counterparts. Whilst no one has actually used them since 1945 the threat (including error or miscalculation) remains, and every government worries about loss of stnding if they don't keep theirs.
My saggested advice for disarmers would be to work on public opinion in nuclear armed countries by proposing referendums on disarmament, by stages (thereby pressing even the authoritarian regimes). Do not worry if the referendums are never actually held, let alone won, but focus attention on the danger to survival and keep controversial moral appeals out.
In the end, we shall have to take on board the realities of modern warfare - an essential element of modernity - whilst tackling social problems like family breakdown or addiction. Bleating about traditional 'glue that holds society together' is not good enough.