Missile Defense = "Hitting a bullet with a bullet."
Instead of attempting to "hit a bullet with a bullet", they should sneak up from behind thus making the relative closing speed much closer to zero (as opposed to "Plaid" x 2). It would make the interception very nearly trivial, plus they could immediately try again if they missed the first time.
It's a much better concept.
The only immediately-obvious rebuttal that I can think of is that the enemy warhead is probably on the pointy end. So you'd want to do something energetic enough to disable that end, depending on where the interception is being made. If it's mid-Pacific and still boosting, then maybe it's enough to simply cause it to miss the continent.