Flight time from 300 miles away is
300 miles
——————— = 0.048 hours = 174 second
6200 mile/hour
So the ship has less the 3 minutes to defend itself. And there is nothing that is gong to shoot down a missile going mach 8. At 30 knts the ship will be within a 9000 feet of where it was at launch. I would think flight software could solve a 9000 foot problem.
A mach 1 missile launched from the same distance would need to solve a 15 mile problem. A mach 8 air breathing missile is a game changer.
1) You would have to detect and accurately know the precise coordinates of the target from 300 miles away, and do so before launch.
B) The mach 6 missile would have to be able to detect the exact location of the target while traveling at, well, mach 6. Atmospheric heating around the missile would preclude the use of infrared sensors for target detection, and ionization of the air around the missile would preclude the use of active radar for target detection. So how is the missile going to determine the corrections necessary for a hit?
III) Assuming that the missile does have a means for terminal detection of the target, at mach 6 there isn't much course correction maneuvering the missile can do, so we're back to 1) above, you need a near perfect firing solution before launch.
Which all boils down to a missile that is more suited for a nuclear first strike, not conventional warfare.