Re: Mach 5-6 Russkie missiles
The point about an aircraft carrier battle group is that it has an aircraft carrier. So it operates defence in depth.
This means that individual ships have point air defence capability, and then there are area AAW capable ships to defend the whole task force.
But firing missiles at short range requires being at short range. Well to get to short range of a carrier group requires driving along slowly through a zone where its aircraft can fly along quickly. If you've shot down all its planes, then a carrier group will be running away, terribly fast - as there's no longer any point in it being there. If you haven't shot down all its planes, then you're probably busy running away terribly fast, before they destroy you.
And firing off missiles at 600nm range requires a target. Which requires getting something with a radar on it significantly closer, in order to know where to aim your expensive, often not replaceable at sea, missiles. That platform then has to survive the air component of the carrier group in order to communicate. The ocean is big - and just a target of over-there guv isn't really enough for effective use of weapons.
You also neglect to remember that carrier groups often have "friends" underwater. If any navy regards their own submarine service completely as friends...