The technology is totally feasible, and not even that complex - it's just that it's pretty much the most evil thing man could devise.
"After delivering all its warheads, the missile could then spend weeks flying over populated areas at low altitudes, causing tremendous ground damage with its shock wave and radiation from its unshielded reactor. When it finally lost enough power to fly, and crash-landed, the engine would have a good chance of spewing deadly radiation for months to come."
"Too provocative" was a pretty mild way of putting it.