When the AI surrenders, there is generally not much left. Do you really want to chase down scattered AFV crews and infantry squads with only 1 or 2 men left?
The way it's working out is more the parent unit owns both, but the Avengers still get farmed out as required. Case in point while the PATRIOT batteries in Korea all live near very sensitive things, the Avengers are based out of Camp Casey with the rest of the US ground forces. This does not preclude the point defense role, but it was not as cut and dried as being linked together.