I just finished re-reading Carl Sagan's Pale Blue Dot, in which he devotes a chapter to this subject. His conclusion is that, at our current level of civilizational maturity, we're better off crossing our fingers rather than learning how to redirect asteroids, since the technology required to save the planet from a massive impact is exactly the same as that used to conduct asteroid bombardment.
I'm having trouble imagining a scenario where asteroid bombardment makes any sense in a world where nukes and ICBMs exist. Even factoring in the inconvenience of radiation it doesn't work. Too complicated, too expensive, too slow, anyone who could do it now or in the future will either have nukes or the ability to quickly acquire them.
His concern is less about global escalation to some nuke++ level of WMD, but more around rogue states or doomsday cults getting access to control systems for asteroid deflection defenses. It isn't implausible: technologically sophisticated death cults exist (e.g. Mum Shinrikyo, North Korea, ISIS/Daesh), important stuff gets hacked all the time, and I doubt most on HN would be comfortable saying "well this stuff will be really secure."
His proposed method of asteroid deflection is actually based on using nuclear explosions to shift orbits minutely far in advance of impact. Timing makes it pretty useless for war (as you point out), but very effective indeed for creating a precisely scheduled apocalypse and the global collapse and panic that likely precedes it.
