The US Navy is at the top of its game and has no place to go but down. Predicting what future tactics and technologies will appear to threaten that supremacy is a risky business. The past is a prologue, not an accurate prediction of the future. But taking a look at how navies in the past dealt with the problem provides insight into solutions, as well as unsettling patterns that may occur once more.
For example, armored ships were not a panacea in the mid 19th century. There were seaworthiness and cost problems. Armor really only worked if steam propulsion was used (otherwise battle damage would tend to destroy masts, sails, and mobility.) Steam power had serious disadvantages. Fuel now became a serious constraint and steam navies were more expensive to run. As a result, the USN backed off from steam and armor for several decades after the Civil War.
New technologies are often, initially, more trouble than they are worth. Steam and the torpedo required several decades of tweaking before they were ready for prime time. Same thing with smart bombs and air-to-air missiles.
There are also problems with asymmetrical warfare, which tends to work both ways. Had the Germans thought asymmetrically before World War I or World War II, the Allied navies would have had to face more, and better, German submarines earlier. While you can't win a naval war with just submarines, you can prevent a superior naval power from maintaining sea control.
Don't forget that quantity had a quality all its own. This is something the USN has long been aware of, from the masses of Japanese cruise missiles (Kamikazes) off Okinawa to the Cold War nightmare of the Russians doing an even larger Okinawa on an American fleet. And now China is buying up a lot of those Russian missiles.
Navy's have an advantage in that operating at sea for long periods is pretty close to wartime conditions. One major thing that's still missing is realistic damage control experience (from enemy weapons, not accidents.) As was discovered in the 1980s (Falklands casualties, plus the USS Stark, Roberts, Princeton and Inchon getting hit in the Gulf between 1986 and 1991), peacetime estimates often come up a little short compared to wartime realities.
Quantity does, in the end, usually prevail. Britain ruled the seas for centuries because they had more ships than anyone else and kept them at sea more than anyone else. Britain ceded that sea control when the USN took over the task of patrolling the world's seas with a large fleet.
But the navy searches through past, and likely future experiences mainly to avoid deadly surprises in some future naval battle. Remaining the top naval power is a lot easier than safeguarding the lives of sailors in future naval battles.
How Does the World's Most Powerful Navy Keep it That Way?