Edward Teller, the inventor of the hydrogen bomb and longtime head of Los Alamos National Laboratory, believed it was possible and even a good idea to place 1 gigaton yield warheads on orbital platforms for asteroid defense.
It might seem outlandish to us, but then again, so would a hydrogen bomb.
He's not entirely wrong. If we had a good way of getting a warhead to an incoming asteroid, it'd be a great safety mechanism. Unfortunately, today, there is no one trustworthy to put that sort of weaponry into somewhere that would allow it to strike any location on earth with less than a few minutes warning. Especially since something of that yield would devastate a large portion of earth.
Imagine you we’re an insane billionaire with the ability to launch objects into say a lunar distance orbit. It wouldn’t require a lot of cold gas to drop some rods onto any spot on earth, and it would be undetectable until the explosion happens.
As space becomes easier to access the risk increases exponentially.
It would require quite a lot of it because you need to significantly change the orbit, especially if you want it to still be plenty fast on impact.
And it doesn't make much sense either. A billionaire can just pay a few millions to send a guy in a car bomb or a cessna full of explosives. It's way simpler and just as undetectable until the explosion happens.
Nuclear weapons which are optimized for wide surface area destruction or bunker busting are not very effective. Nuclear bombs like any bomb can be tuned to produce a variety of effects. See Nuclear shaped charges https://en.wikipedia.org/wiki/Nuclear_shaped_charge
A powerful nuke could certainly alter an asteroid's trajectory. However, most of the energy would be wasted. It'd be better to use a nuclear propulsion reactor strapped to the side of the asteroid to direct it more accurately, but we don't have that technology today, whereas we do know how to make big bombs.
Also, the idea of changing an asteroid's trajectory just before it hits the Earth is crazy. You need much more warning, because even a big bomb isn't going to move the asteroid that much, so you need to use it long before it's projected to collide.
It might seem outlandish to us, but then again, so would a hydrogen bomb.