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Opponents could make armor penetrating missiles much faster than we could build, or restore to service, armored battleships.

Missiles? Hardly. It takes a long time to develop a new missile, particularly a large one that would have enough warhead - with heavy, armored case - to penetrate heavy armor. We are still using missiles developed 40 years ago (Harpoon, Tomahawk) and so are others (Exocet, Silkworm).

Could it be done? Eventually. Then they would face the problem of developing, building, stockpiling, deploying (in large quantities and great density to have a chance to do enough damage), maintaining, and training with multi-million dollar missiles that are only effective against a few specialized ships.

I never advocated building more battleships. Restoring to service our existing ones would not take that long (see the 80's when they did it). And if potential adversaries spent the resources to develop effective, armor-piercing, heavy missiles (Musashi took 17 hits by heavy armor-piercing bombs, but it was the 13 torpedo hits that sunk her, so it would take a lot of missiles), then we could laugh all the way to the bank when we just retired the battleships again. Economic warfare at its most effective.