That’s…literally how hardkill APS works. CIWS takes the same approach but uses a rotary cannon instead. The issue ain’t putting a missile in the path of the other missile. It’s in having enough time to do so. This is why the US concluded that the most effective way to intercept an ICBM is to destroy it before it finishes its acceleration stages. Ballistics is a known quantity.
Still aren’t convincing that you know what the hell you’re talking about.