You have linked high speed with a precision problem, when the reverse can be true. You also introduced a premise that the target position would only be known at launch and then lost over many minutes so requiring a new search. Modern targeting information can come from off-board sources and form part of the updated guidance solution.
The Pershing example from nearly 50 years ago was to demonstrate the controllability and the ability for sensors to survive re-entry. What was incredibly difficult all those years ago is considerably easier now - the hard miles have been done. The Soviet Union's own anti-ship ballistic missile was fielded in the late 70's and had a CEP of around 300m against a ship so relied on a nuclear tip to close the final margin of error. Given modern systems and suitable money they could do much better today; but for money and effort you have to look at the Chinese.
As for the politics of the US devastating a country that managed to hit a CVN during a conflict, well that's not my area of expertise. I would like to hope that the US could take and accept a hit on a CVN in harms way doing its job, without triggering total war - but you never know.
The USN has flexed its muscles with CVNs rather effectively for many decades in a rather one-sided use of firepower. It is understandable that potential adversaries have worked hard to provide a credible counter. Your point about them providing an effective area denial weapon is well-made and reflects current USN thinking. The countermeasure cycle is without end.