I would say western anti missile defenses don't really work because their chief opponents have superior weapons

The Iron Dome, the magnum opus of western middle defense systems regularly fails to intercept unguided, subsonic rockets that are incapable of taking evasive action. I would not say that the Iron Dome fails because Hamas has superior missiles, it fails because shooting a bullet with a bullet is a near impossible task. Also, ICBM interception is close to a fantasy right now. The GMD works around 40% of the time in tests, the arrow 3 does not work at all, the A-235 has only been tested a few times (not in real world conditions either), and China doesn't have an anti ICBM system at all.