Spielberg chose to shoot this movie the way he might if he were really there filming what took place in Krakow. That means a lot of the narrative bells and whistles go out the window, leaving us with a just-the-facts-ma'am narrative.
We get some crosscutting between scenes for dramatic effect, as when Schindler settles into his new pad while its former Jewish homeowners are crammed into a tiny room with 50 other people in the ghetto. We flash forward to the present day in the last scene, when the real-life survivors honor Schindler at his grave.
But that's still in keeping with third-person omniscient narrative, and the rest of the film sticks pretty much to a straightforward presentation of what happened in a more-or-less linear fashion. Spielberg uses the freedom of the camera to focus on different characters when their experiences take the forefront, but he mostly focuses either on Schindler or on the workers in the camp.
As our protagonists, that's where the focus should stay. Spielberg wants us to feel that we're there watching this unfold before us, and as a result to have a greater appreciation for the horrors that took place. Getting fancy with the narrative would just undo all of that. So he plays it straight, adds a documentary sheen to it all, and lets the story tell itself without getting in the way.