The thing is we CAN see half-mile wide asteroids. Granted we're not tracking everything out there. This rock was nothing to be concerned about and NASA would be wasting time looking for stuff like this. We get hit by this kind of thing all of the time this one just happened to happen over a populated area.
You missed my point, one of these smaller ones that fly under the radar could strike a bigger one that we think will miss us and change its trajectory slightly to a trajectory that would not be conducive to the survival of the human race. That is why developing new tech to track these little guys along with better computers to look at the course of all the space rocks in our solar system matters in the coming decades.
This isn't a situation where brute force is the optimal solution. You can't really blow up an asteroid like in the movies -- and if you could, it could actually make things worse, because all that mass would still be on the same collision course for Earth, and it would come down spread out far more widely.
Given we don't have anti matter weapons yet or anything that can explode in the 200 gigaton range its a bit speculative as to if the pieces left would be small enough to wipe out life on Earth and as I made clear such an weapon would only make sense assuming we only figure out the rock is headed toward Earth at the last minute and can't organize anything else in time or everything we organize fails to work.
Even if it doesn't work all that well I would rather let the atmosphere work its thing on tens of thousands of pieces of rock instead of dealing with just one half mile wide rock.