The launch pads are right on the coast. This means that an Aegis could be located 13 miles away, although getting out past artillery range would be smarter, lets say 25 nm.
At 25 nm, the Aegis might not even require an SM3 to knock down the missiles (using the SM2), as the launch would likely climb up and over teh Aegis position.
Only the SM-3 can intercept a ballistic missile, and the intercept point MUST BE OUTSIDE THE ATMOSPHERE (the actual seeker and final stage are not aerodynamic.)
The problem is, fired near the launch point, an SM-3 Block I can't catch up to a ballistic missile in a tail chase; it's too small and too slow.
Unless the missile launches fail, everyone is just going to be waving at them as they go by, even if they are launched over Japan.
Boost phase intercept only would work with a ginormous missile - one was under development (the KEI) but it was canceled. It wouldn't have fit on a US Navy surface ship.
Rock & Roll !