Having reread this, I discovered another mistake the captain made - assuming that a fething DESTROYER would be unseen by a submarine simply because they continued passive detection. Um, they were going essentially flank speed to get to the "island" to effect a rescue - the prop noise alone would have alerted every sub in the northeast Pacific they were there. The fact that the distress call specifically mentioned a threat from underwater should have had him banging away at the sonar to begin with, even if the Chinese in the area might've perked up (they would have received the distress call as well).
Basically, the kaiju still would've fucked them raw, but they'd have had a better chance if the captain wasn't incompetent.