If you ‘nuke’ an asteroid, where will all those shattered pieces go?................
Some of the fragments that are ejected tangentially to earths orbit will likely be threats themselves when the earth passes through that space one year later.
Although, I expect the experts who propose this would suggest that the fragments will be too small to cause serious damage
They will enter the moon's gravitational pull and form a big, beautiful ring system that will be visible from Earth.