The main problem with anti-missile systems is that nuclear re-entry vehicles are just too small and too fast to get a hit on with current technology, right?

So why don't we just use small nukes for defense? Even 1 kt would make your margin of error for interception larger by orders of magnitude, so designing a missile that can get within the blast radius of an incoming MIRV should be trivial compared to designing one that can reliably score a direct hit. The defense would be way cheaper than the attack, since the missile doesn't need to go around the world and the warhead is way smaller.

Sure, you're detonating a nuke over your own land, but compared to what it's stopping...