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How could the ship not have seen this coming, and gotten out of the way? The destroyer exists to find things above, on, or in the sea and uh, destroy them.

They are the shield of Zeus.

https://en.wikipedia.org/wiki/Arleigh_Burke-class_destroyer

The Arleigh Burke class of guided missile destroyers (DDGs) is the United States Navy's first class of destroyer built around the Aegis Combat System and the SPY-1D multifunction passive electronically scanned array radar. The class is named for Admiral Arleigh Burke, the most famous American destroyer officer of World War II, and later Chief of Naval Operations. The class leader, USS Arleigh Burke, was commissioned during Admiral Burke's lifetime.

These warships were designed as multimission destroyers[5] to fit the antiaircraft warfare (AAW) role with their powerful Aegis radar and surface-to-air missiles; antisubmarine warfare (ASW), with their towed sonar array, anti-submarine rockets, and ASW helicopter; antisurface warfare (ASuW) with their Harpoon missile launcher; and strategic land strike role with their Tomahawk missiles. With upgrades to their AN/SPY-1 phased radar systems and their associated missile payloads as part of the Aegis Ballistic Missile Defense System, the ships of this class have also begun to demonstrate some promise as mobile antiballistic missile and anti-satellite weaponry platforms. Some versions of the class no longer have the towed sonar, or Harpoon missile launcher. Their hull and superstructure were designed to have a reduced radar cross section.[8]

The first ship of the class was commissioned on 4 July 1991. With the decommissioning of the last Spruance-class destroyer, USS Cushing, on 21 September 2005, the Arleigh Burke-class ships became the U.S. Navy's only active destroyers; the class has the longest production run for any post-World War II U.S. Navy surface combatant.[9] Besides the 62 vessels of this class (comprising 21 of Flight I, 7 of Flight II and 34 of Flight IIA) in service by 2016, up to a further 42 (of Flight III) have been envisioned.

For FWIW department:
The Fitz was on ABM (she was packing the Standard Missile-3 (SM-3) Block IIA)picket duty to protect Tokyo and surrounding areas from anything the Norks would sling that way.
She operates in a restricted area (off limits to normal commercial traffic) usually sailing in a “Box”, she may even been hove to. That restricted area was breached by the Crystal, the Fitz may have been thinking she was in “Protected waters”, the Crystal made a last minute port turn into the Fitz