Nowadays, there are no battleships in service and cruisers and destroyers are of similar size and are mostly used for defending aircraft carriers. For that purpose, US cruisers and destroyers rely on sophisticated radar, an array of missiles and short-range cannons against attacks from the air, with sonar and torpedoes against enemy submarines. In a pinch, even though US destroyers and cruisers have little or no armor, they are expected to absorb or divert missile or torpedo attacks so as to protect carriers.
You are correct about our need for more naval surface combat vessels. Against China, the best US strategy will rely heavily on cutting off China's sea trade. Much of that will be done through economic warfare, but having USN aircraft carrier task forces and even single destroyers and frigates prowling the world's oceans will back up our diplomatic demands.
Notably, upgrades to the longest range US Navy missiles on cruisers and destroyers now make them capable of striking everything from satellites, to incoming ballistic missiles, to enemy ships almost a hundred miles away. Connectivity with drones and combat aircraft will permit even relatively small US Naval vessels to direct air attacks from hundreds or thousands of miles away.
If done properly and with severity, trade interdiction and economic warfare will collapse China's economy into a severe depression, with mass unemployment and potential starvation. This will cause the CCP to be overthrown, with China soon breaking up into several regional states.
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When you look at the results of Millenium Challenge 2002, what does it say about the survival of the US surface fleet, when China has infinitely more capacity than 2002 Iran ?
All you have to do is look at the missile coverage from this map, and the problem for surface ships becomes clear. What is the plan if a supposed blockade cannot be maintained ?
Fact is, the US is no longer capable of exerting this sort of power. And it is time to put aside the delusions and start making decision based on some sort of connection and attachment to reality.