I don't think you're wrong broadly, though I want to add that the particular interceptor warheads were relatively small and nukes detonated in the upper atmosphere generally don't do much to stuff on the ground. There's not enough material to create significant fallout so it's just a mild EMP and even milder pressure wave

Interesting post. It made me think that a manned Navy of individual high value ships becomes essentially useless if you can take out a 13 billion dollar carrier with a 3 billion dollar missile.

It becomes a war of financial attrition at that point.