Earlier quoted context omitted.
Can a large ship, or any ship, intercept a hypersonic missile? Because that's the reality of today.
Yes. Patriot has intercepted Kinzals in Ukraine (and older versions of Patriot at that), so the tech is well established. SM3/SM6 missiles on Aegis equipped ships can defend themselves against hypersonic missiles.
It's a similar story for SM-2/3, in the Red Sea they faced massive interceptor depletion and had to leave, and even then many missiles were not intercepted, we just got lucky that they missed.