(or "A Cast Of Millions")
Looking at 'Our Army At War', as collected in the 'Showcase Presents' line of trade paperbacks, is a little unfair in some ways when trying to analyze the storytelling engine of the book. The comic was always an anthology, a mix of recurring features like "Sergeant Rock" (who eventually took over the book entirely, a few hundred issues down the line) and a collection of unrelated short stories about various different individuals in various different wars throughout history. Since DC has already cannibalized most of the recurring features from 'Our Army at War' (and, for that matter, from its war comics in general) and presented them out of context, seeing this single volume of stories from the very beginning of the series' run gives an impression that might not represent the series as a whole. We don't see any recurring characters. For that matter, we don't even necessarily spend all our time in the same war; 'Our Army' jumps around from Korea to WWII to the Civil War to the Revolutionary War, even if it does spend most of its time centered around the Axis powers. It's worth beginning with that as a caveat, because remembering that the series will eventually get around to having a cast of semi-regular characters tells us a lot about the stories we see here.
Because the whole point of a cast of recurring characters--indeed, the whole point of a storytelling engine--is that it makes coming up with ideas easier. Having to come up with a new group of soldiers every single time you tell a story is exhausting. It consumes the time and energy that the writer could be using to do other things. If he already knows Hans von Hammer inside and out, and if the Enemy Ace is an interesting enough character to spark ideas simply by reading his character bible, then he can get stories done quicker and easier. Which, when you're writing four stories an issue on something like three titles a month, is a very useful thing.
But in a large, sprawling story like World War II (or an even larger, even more sprawling story like the history of warfare) you can't always work a cast of recurring characters in. Sergeant Rock fights in the European theatre of World War II. Just getting him over to the Pacific for a story you've wanted to tell about Okinawa is a difficult enough task, let alone working him into a story about Korea or World War I. Sometimes, you expend less energy by coming up with a new character than you do by working the old ones into your existing story. Which is where it's useful to have an anthology series. The war itself sparks so many ideas that one character can't possibly tell all of its stories. Mailmen and cooks have stories to tell just the same way that World War I fighter pilots do...even if they don't have quite so many.
And of course, there's one type of story that simply can't be told easily by a cast of recurring characters, and it's one that crops up quite frequently in these books. Stories where the main character dies at the end are a staple of war comics; heroic sacrifice is a theme of fiction about warfare, and there are limits to the number of times you can tell a story like that in a book with a regular cast. Either the cast winds up dying off, which severely limits future storytelling possibilities, or you have to introduce a secondary character just so you can kill them off...at which point, you're already doing all the work of coming up with a new character anyway.
Which is why, despite the introduction of many great ongoing stories within DC's war comics, the anthology still went strong for a long time (and arguably still goes strong today; Garth Ennis' 'War Stories' is essentially a descendant of 'Our Army At War'.) Because ultimately, writers use a storytelling engine to make their lives easier, not simply because it's there.