You don’t take the satellites out in this case by direct missile impacts. You fry electronics by increasing the radiation in space. A nuclear blast puts out tons of high energy protons and electrons. These are trapped in the earths magnetic field and live for years there. These satellite electronics are bombarded by these every time they pass through the field, in LEO that could be large percentages of the orbits. They won’t survive beyond a few days if that.
Agree with what you are saying but think we could solve that problem.
The only way to kill Forbin’s Colossus was to make it kill itself.