The US government is developing a "layered" defense that aims to destroy enemy missiles at different stages of their trajectory. So far, the most advanced layer is mid- course defense, which targets warheads high above the atmosphere some 10 to 15 minutes after launch.
But it is much easier to detect and damage rockets while they are firing their boosters, than to target smaller, coasting warheads. Destroying missiles in their boost phase would also drop any hazardous debris, such as nuclear or biological material, close to the attacker's territory.