Obviously, someone has to be in command on the bridge at all times, but it does not have to be the captain the whole time. That's what watch commanders are for, right? The guy cleaning toilets does not need two more guys backing him up for the 2nd and 3rd shift. Dirty toilets wait until he rolls out of his bunk, or until the captain eats a volatile burrito, and someone wakes the toilets guy up to deal with that specific problem outside of regular duty hours.
Command staff already needs to have enough redundancy to operate the ship if an unlucky hit takes out the entire regular command, just as a requirement of being a war vessel. In theory, that Junior 2nd Lt. should be able to limp back in to port after everyone else in the chain of command is killed, so the Navy can send it back out with a fresh crew.
Surely, there's a person whose function is to alert person X when situation Y happens, so that person X is not expected to be awake and alert and staring at green lights for N continuous hours, and then exhausted or asleep when one of them turns red?
That isn't how it works.
So there are all kinds of functional roles in the Navy (and I'm going off of submarines since that it was my experience was in), roles having to do with operating the sonar equipment, IT/comms equipment, torpedoes, and the engine room. So these people will be on watch (hourly logs, monitoring system conditions, etc.) and then after they are relieved they'll do whatever maintenance and cleaning they are assigned to. There is not a "clean-the-toilets" job role.
In AEW, specialization rules everything, so the toilets are cleaned only by a specialist toilet cleaner, and specialist toilet cleaners only clean toilets. If you try to shoehorn AEW onto a ship, you only need one toilets guy, because having clean toilets is important, but not so important that it has to be done 24-7.
It is an open question whether it would be more efficient to have 3 radio operators providing 24-7 coverage on the radios during their duty hours and doing other jobs when they are off watch, thus giving them 16-hour workdays divided up into 8-hours of "important" work and 8-hours of "grunt/scut" work, or to have 2 radio operators on watch 12 hours each, and one specialist cleaner taking up that extra 8 hours in that bunk, cleaning toilets 12 hours a day. Is that last 4 hours of work squeezed into the day okay if it requires no dedication or focus?
Most watch stations take months of training to not only get qualified but also for the command to have enough confidence in you to stand the watch. I myself stood a regular 12 hour rotation during times we where on the surface because we had only 2 qualified operators and the rate that actually owned the equipment was undermanned so they could not provide bodies. There are very rarely extra people to do grunt work you do that in your off watch time when you are not studying, qualifying, or doing maintenance. Very frequently commands will care about filling the watch bill over a person not just being qualified but also competent enough to stand a watch, thus accidents happen due to negligence and ineptitude.
Even so, it's still 8 hours of sleep per 24 hours, which is adequate, even when only being able to take 6 at a time makes it somehow seem worse. And I have a sneaking suspicion that it only exists because the Navy found that sailors were useless after the 12th hour of working, so decided to set the workday to 12 hours, and just make the whole duty cycle 18 hours. I'm guessing that people on that schedule stop being very effective after just 9 hours of wakefulness. But I'm no somnologist.