FWIW, there has been a number of nuclear explosion tests in our atmosphere: https://en.wikipedia.org/wiki/Tsar_Bomba
Further your ignoring submarines and early proximity detonation on the nukes. The most likely result of building such a system is an early nuclear EMP clearing orbit before the nukes get through anyway.
How many satellites do you need to reach that kind of coverage? And how many interceptors per satellite to hit everything from one or more nuclear subs launching from the same location near a major city. How long does it take you to react without risking false positives making the system useless etc.
The problem just gets ugly fast.
The number of interceptors per satellite was unclear but this USAF captain said "composite rocket motor and micro-missile system capable of fielding a rocket pod of 100 interceptors at a cost of approximately $60,000 per micro-missile" https://www.airuniversity.af.edu/Wild-Blue-Yonder/Article-Di...
It took out 3 satellites initially (there were very few at the time)
> In the months that followed, these man-made radiation belts eventually caused six or more satellites to fail
Today, with modern nukes, if one was intentional, they could disrupt or destroy the space ecosystem
Really any of the nuclear material will just disperse into the atmosphere relatively harmlessly, especially if it's somewhere over an ocean. Plutonium in seawater measures in the parts per billion anyway.
Having several pounds of plutonium burn up in the atmosphere just means it will be spread over a very wide area which is much worse than a chunk of it falling somewhere.
U-235 is basically harmless.