Impossible? What part of producing cobalt 60 by irradiating cobalt 59 with neutrons is impossible? What kind of bomb do you think I'm talking about here? I'm talking about a very dirty type of nuclear or thermonuclear device that is possible, but is so poisonous that to use it is suicide.
Here is a Federation of American Scientists report that includes estimates of the damage that can be done by one piece of cobalt of the kind that is used to irradiate food:
Article They are talking about making the entire borough of Manhattan uninhabitable for years. This is just from using TNT to scatter a few pounds of the material.
I don't know how anyone could seriously say that these things are impossible to construct. You put a big honking piece of cobalt metal, alloy containing cobalt, or a cobalt compound next to a nuclear device and touch it off. If you can throw the weight and don't feel like refining the ore, just stuff your missile with the ore. So they don't set the atmosphere on fire. They don't have to. They do generate just about as much cobalt-60 as the missile or other transport can ship cobalt, and that can be a lot of tons of cobalt-60, when a few pounds can cause dangerous contamination of a thousand square kilometers. This stuff is so pernicious that if China sets one off in Kansas, it will make people sick in China.
Wiki Article
Google search for "cobalt bomb"
If Clockwork and Light don't understand that a cobalt device works by contaminating large areas of land with a powerful gamma emitter with a half-life of 5.27 years, that definitely hurts their credibility. This is not practical for someone intent on invasion but it would be practical for someone who would tolerate large losses of their own people to completely obliterate an opponent.