The thing that always got me about the 'night shift' was the notion that nothing important ever happened during them.
There were at least a few episodes that showed things happening at night. Warhead
had Acting Captain Kim changing course to a planet before calling his boss, Chakotay, and informing him of the change. Chakotay called Janeway, who was sleeping.
I think the general idea was that things can happen on all three shifts, but if something important happens or if their heading dictates that they will arrive at a certain planet at a certain time, then the senior officers would adjust their schedules so that they were awake for that event. In the interests of expediency (and because the show is technically about our heroes and not the backshift folk) they just show our heroes as the ones awake all the time. I can grant latitude for not having to show this sequence of events all that frequently.
TNG's Data's Day
also showed this to be the case. Data had command of the night watch, Riker had command of the day watch, and Worf had command of the evening watch. Picard, even though he's the Captain, would simply be on the bridge whenever he was needed to be, be it day, night, whenever.
A final example is Star Trek VI, when Christian Slater wakes up Sulu in his quarters to inform him of the transmission from Starfleet.