The way I heard it, Walter was the only actor seen for the role. He gave his reading and they hired him. [I think that's true of Walter, George, and Nichelle; correct me if I'm wrong.] I think he interprets that as a mark of pride, because they cast him on the spot, but I wonder if they put enough time and care into the casting process. I wonder if he would have won a more competitive audition.
You hear about important roles where 200 actors are read for the part, with many call-backs to work through, and the job goes to what amounts to a tournament winner, a champion who was just right and really nailed it. When that happens, you get a good performance. I can see Jimmy Doohan possibly winning a competitive audition for Scotty, but for our other five supporting parts, namely Sulu, Uhura, Chekov, Rand, and Chapel, it doesn't seem like we got tournament-winning material. For some, it was literally first come, first served.