"Every enlisted man in the Navy only gets 4-5 hours of a sleep a night" seems to be a common anecdote service-wide, including from people I know personally who served.
Also, "nights" are not a real thing, not in the biological sense.
In the surface ship nuclear power plant world where there is no air conditioning, you can't stand watch for more than 5 hours, which means 4 5s and one 4 hour watch. Think you stand the same watch every day? Nope, not enough people. You normally stand 1 on 2 off (5 and dimes) or one on 3 off (5 and 15s). This puts your sleep window at different spots every night.
Subs are air conditioned, so they can stand either 6 and 6s or less commonly 6 and 12s. Their lives are generally worse in every way.
Except they all like smelling each other farts and sharing beds, so it works out.
I think the high operational requirements expose a culture/procedural/values problem of the shipboard Navy overall, it's just particular visible in 7th fleet because of the unsustainability of the workload.
I obviously haven't done an A/B study, but I would figure that having periods of crunch time (long or short) with periods of sane time would both keep military units in practice for when they do need to be up for three days on four hours of sleep AND let them train/maintain/not crash their ships into other ships.
But I doubt that the culture described in TFA, and this thread evolved in any way but organically.
Cultural Problem IMO. My boss likes to say that the military takes their young officers and train the common sense out of them. Personally I blame the service academies for what amounts to 4 years of legalized harassment. First three years are all about getting harassed. The last year is about dishing out the harassment. Then they get a degree to justify the whole thing.