Well, of course it takes time. But, then, you've gotta realize that it's only when it's moving exactly parallel to you.
If you're moving antiparallel to it, you'll be over it in seconds. Relativistic speed, right, Mike?
I don't see the point in it having huge guns. It's not a fleet, it's an aircraft carrier. It can have CIWS and anti-ship weapons, even, but as soon as it comes to having a million guns, it's really pointless. At that point, you don't need the fighter squadron, so you can eliminate that aspect, which would cut its role to something else.
Point of this post: Leave it to the fighters. Concentrate on shooting the missiles down!