There are theoretical advantages to boost phase intercept. They are not usually meaningful. You rarely can shoot one down at that time - it is too far away. If you can, you virtually never will get permission to shoot. And you cannot know if it a test or a real war shot when it comes out of the launcher - so a decision is not really meaningful if the President was right beside you as you tracked it. But you normally do NOT track it at all - other sensors see the heat plume and sometimes other things. But unless a ship or plane with special radar is in the right place, you won't be getting anything like tracking data for your ABM system in the boost phase. Theories to the contrary were studies and proposals, not operational systems.