Third Person (Limited Omniscient) / Joe
Despite the fact that we're always inside Joe's head, Johnny Got His Gun is told in a third-person voice, meaning that Joe never refers to himself as "I" except in direct thoughts. It's a bit strange, because clearly we are getting Joe's perspective on things, yet there's still this odd narrating voice that insists on referring to Joe as "he."
In fact, a lot of the time, we're getting what are clearly Joe's thoughts through this third-person filter. Like here: "Oh Jesus Christ they'd cut off his left arm" (3.6). Or here: "Maybe nothing was real not even himself oh god and wouldn't that be wonderful" (8.15). The narrator isn't the one who thinks "Oh Jesus Christ" or "oh god and wouldn't that be wonderful," and yet it's not a direct thought, because then it would read: "Oh Jesus Christ they'd cut off my left arm."
This is what people who spend a lot of time in libraries call free indirect discourse.
So why wouldn't Dalton Trumbo just write the novel in the first person? Let's take the first line of the book as an example. It starts with this line: "He wished the phone would stop ringing." In first person, this would become: "I wished the phone would stop ringing."
Okay. The difference is really subtle, but in the first person, Joe has a lot more control over the situation. Sure, he still can't stop the phone from ringing, but he's still asserting that he as a person wishes that it would. In the third person, it's as if things are happening to Joe as a passive agent rather than Joe doing those things actively; not only is the annoying phone ringing, but all Joe can do is wish that it would stop.
Given how the conflict of the book comes to revolve around Joe's helplessness, this seemingly small detail might make a huge difference in how we read the book.
But just to be hypothetical: do you think the book would have been more effective if it had been written in the first person? One thing to consider here is that in the movie and stage adaptations of Johnny Got His Gun (check out our "Best of the Web" section), things do happen in first person. How does it change your experience of the work?