The good points:
- Weapons fuzed for high-altitude air burst, which maximizes the damage area at the expense of not being able to kill hardened targets, are not going to produce dangerous fallout.
- The typical warhead now is significantly smaller than the multi-megaton ones that were typical during the era of the Cuban Missile Crisis.
The large assumptions:
- Hardened, remote military targets will soak up a lot of warheads that could otherwise be targeted to wreck cities or general-purpose infrastructure.
- Civilization will only regress to an early-20th-century level after every oil refinery has been destroyed and the surrounding populations decimated.
That last pair of assumptions in particular raises my eyebrows:
"To put this into perspective, there are currently about 1,200 international airports and 732 oil refineries worldwide. Allocating a single warhead to each of these would leave only a thousand or so for every single other target on the planet."
and
"Most people even in major urban areas would survive the initial attack, along with a surprising amount of infrastructure. This isn’t to minimize the effects, as it would be a humanitarian catastrophe unprecedented in human history, as the global economy breaks down and regions are pushed back on their own resources. This could easily kill more people than the war itself, particularly in densely-populated areas, but I would expect things to stabilize at a technology level of maybe the late 19th/early 20th century and start back up."
It hardly matters if most people survived the initial attack if all the oil refineries are gone, along with all the infrastructure within a couple miles of each oil refinery. Early 20th century technology supported fewer than 2 billion people, most of those being people who already knew how to farm without artificial fertilizers. Today we are nearly 8 billion and a much smaller fraction have any experience farming. A nuclear war that globally knocks technology back to the early 20th century, even for "only" a decade or so, would lead to the death of most people now alive. At that point I'm skeptical that there would be enough survivors to sustain even as much specialization of labor as found in the early 20th century industrialized economies. Technology level and population could fall much further.