Of course, things start to get a bit dicey when you add not so rational nuclear powers in to the mix (e.g. North Korea), or diversion of nuclear bombs to not so rational 'non-state actors'.
I feel you, but that assumption is where this argument diverges from reality.
It would take more time than a nuclear exchange but it is possible to inflict comparable levels of destruction through conventional warfare if you have multiple nations sending millions of humans into battle as part of a war that drags on.
[0]. https://ourworldindata.org/war-and-peace-after-1945/ [1]. http://www.fallen.io/ww2/
Also, advances in medicine have significantly reduced the number of deaths in war. It's worth noting that in the American civil war, the vast majority of deaths on both sides were attributed to non-combat disease.
So maybe you have a point, but I doubt that it's as simple as more nukes = less deaths.
This, of course, is not what happened. The Damascus Titan accident did not involve a nuclear weapon being mistakenly, but intentionally, armed. The very real fear was, instead, that the explosion of a damaged missile could accidentally detonate the warhead as well -- or, in a case only slightly better, blast it into radioactive dust.
I'd never considered the risk entailed by the simple existence -- intentional use entirely aside -- of nuclear weapons. Reading the list of (public!) broken arrow incidents is harrowing.
The more feasible way is arms limitation. Let's say you go from having enough nukes to destroy the entire planet to merely having enough to end your opponent's civilization as we know it. But the more alliances means the more enemies or even targets on your own side.
10,000 to 1,000 is relatively easy. 1,000 to 100 is very very hard. <100 will probably never happen :(