@Aplu: problem is that when you look at an object at night, you’re looking at the sunlit side, it’s bright. An object coming in from the Sun direction, you’re looking at the night or dark side of the object in a bright sky, just can’t see it. Radar is only effective so far, the smaller the object, the closer it gets before radar sees it. At the speeds these things fly, they get pretty close time wise before you detect them. It would require a lot of high powered radar to cover the entire sky, which would likely be detrimental to other things.
@sam85geo: If you blow up a 100 tonne asteroid, you now get a buncha rocks heading in pretty much the same trajectory, no such thing as destroying it. mass before equals mass after, just in pieces. Moving in terms of kilometers per second, you won’t affect it’s motion much. These would have to be identified way in advance (perhaps years), then alter its motion slightly so it misses Earth. When you shoot down an aircraft, it still crashes somewhere, doesn’t disappear. Shooting down something that measures in kilometers, it’s still gonna hit. Early diversion is best.