(It's the same on the road; you have to take it as an article of faith that other people will respect your right of way, but at the same time, it makes sense not to go past junctions with waiting cars too quickly, just in case they don't see you. If you get hit, it might not be your fault, but that's little consolation if you're injured or killed.)
Of course, the rules do also say that both ships are responsible for avoiding collisions with the other, and that both are free to maneuver to avoid collision if they are put in extremis by failure to follow the navigation rules.
Unless everyone on both ships was asleep, this statement doesn't have to be true. If anything, it seems eminently plausible the destroyer's crew was playing chicken with the freighter thinking they were playing against a human opponent, when in fact they were dealing with an automated system.
And standing orders were to wake the captain whenever another ship gets within a minimum distance. So the watch had to not only decide to play chicken with the freighter, but not wake the captain when it breached minimum safe distance.
Interesting you should mention this because, IIRC, the book has an aside about ships that (unknowingly) play chicken with lighthouses.
https://en.wikipedia.org/wiki/Lighthouse_and_naval_vessel_ur...
It is true that many COs will try to time their periods of sleep for when the operational tempo is lower as a risk management measure. I can only assume the Fitzgerald's CO had made his risk assessment and figured that it was better to sleep at night than to sleep during the day when the contact density would be even higher.
But for a Navy warship being "approached by other ships" is a fact of life for every hour of every day, you can't always plan your sleep schedule for when you're the only boat on the pond.
But this still relies on the watch team detecting the contact and realizing that it will pass near to the ship, and so again the ship's captain is back to relying on his or her watch team to at least get to that minimal level of competence -- because if they can't rely on the officers on watch to be able to wake them up properly, we're back to captains who can never sleep.