Doesn’t need to be nuclear, but a Mach 9 MIRV a few hundred 150 lb, 2” diameter by 6 foot long tungsten tipped rods coming down at 6000 MPH will shred just about anything. And there’s not much you can do with a destroyer screen to take out such tiny targets (about the size of two baseball bats, stacked end to end, moving at 1.6 miles per second.
That’s the big danger with ICBMs - you can use them for quick deployment of “rod of god” kinetic bombardment weapons. ICBM goes up, warhead orients, and out come the rods. Each with the equivalent energy of 600 cars moving at 60 MPH. Concentrated on a little 2” area. Nothing that floats will stand up to that.
Remember the GPS disruption tests in So Cal? The targets will not be where the Chinese missile are aimed.
What do you believe the response would be, in the event of a launch detection, of a ballistic track intercepting a carrier group? Those in command will defend their assets.