Moreover, even if Aegis fails to intercept it, the manoeuvre to avoid the intercepting missiles in the terminal phase at hypersonic speeds means a huge miss, at least for conventional warheads.
I don't know of any missiles that have enough situational awareness to attempt to actively avoid an interceptor. They might dispense decoys (like the Iskander does), but a hypersonic cruise missile won't have the appropriate radar to detect an incoming interceptor. It might have an ECM/ECCM package that can tell when it's being targeted by a radar system, but that's about it.