The grim logic of a nuclear anti-aircraft missile

Is placing a six-kiloton nuclear warhead on a surface-to-air missile a sensible idea?

It could destroy a broad bomber formation, but the blast and fallout could inflict devastating damage on the city being defended.

A nuclear surface-to-air missile offers a large-area kill against a bomber formation. That advantage is balanced by the danger of detonating a nuclear weapon close to one's own population. The weapon is technically possible but creates a severe defensive paradox.