An Iowa-class battleship's 16" guns could pitch 1.2 tonnes of high explosive with excellent accuracy, for unguided projectiles, out to 30+ km. A Harpoon packs "only" a 200 kg warhead, but with even greater precision, to a range of 120 km. At first glance, those advantages could well balance out.
But here's the kicker: the battleships didn't use their guns, at least not against each other. Sure, there were a few battleship-to-battleship clashes (Wikipedia lists nine) but far more often, battleships were used for shore fire support, and were attacked by bombers, not guns. So why add expensive and heavy armor when you probably won't need it, and it probably won't help much if you do get hit?
Note that cruise missiles can come in low or use top attack, so you'd need armor all over, not just at the waterline, to try to counter them. Gun-era ships focused their armor where it would best prevent the outright loss of the ship (i.e., the waterline), without adding an outrageous amount of mass. Armor belts were typically twice as thick as the deck for WWII battleships; earlier dreadnought-type ships were skewed 3:1 or 4:1. They were not concerned about air attacks, just plunging fire: at long range, shells can come down at a step angle, albeit more often into the water than the ship. As outlined, the heavy beltline armor built for close-range toe-to-toe combat with other battleships rarely served in such a role.
Venturing into speculation, I expect that modern electronic fire control systems are more delicate than the old analog calculators, so they may be vulnerable to shock damage even if their ship was sufficiently armored as to avoid taking on water. Similarly, fragile radars and radios can't really be armored, and without them a ship is helpless in over-the-horizon combat.