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?