Why didn't Van Johnson serve in World War II?

Van Johnson in Battleground (MGM, 1949)

A reader recently asked me why Van Johnson didn't serve in World War II, presumably because I previously wrote about Roy Rogers' and John Wayne's military service (or lack thereof). Van Johnson was mainly an actor but sang and danced in some musicals, most notably Brigadoon (1954) and The Music Man (the 1961 London cast—not the 1957 Broadway cast or the 1962 film). Johnson's studio, MGM, never attempted to turn him into a recording star, so he appeared on a few soundtrack albums and compilations of show tunes but no singles.

One of the reasons that Johnson didn't serve in World War II was that he was in a serious car accident in 1943 during the production of the film A Guy Named Joe. In the crash, Johnson was ejected from the car and thrown head first into a curb, receiving such severe injuries that he had to have a metal plate put in his head.

Afterward, he suffered from severe headaches, had to do exercises to strengthen his right arm, and wore heavy makeup to hide the scars on his face. 

As a result of the accident, Johnson was classified 4-F, which was a classification that usually was given for physical disorders like muscular and bone malformations and hearing problems. (Other actors who were classified 4-F for various physical conditions were Marlon Brando, Errol Flynn, Jackie Gleason, and Gary Cooper.)

It pained Johnson that he wasn't able to serve. In the book Van Johnson: MGM's Golden Boy, author Ronald L. Davis writes: 

Even though he was legitimately disqualified from the draft after his automobile accident, Van was sensitive about not serving in the armed forces, particularly since Jimmy Stewart, Tyrone Power, Gene Autry, Robert Taylor, and so many others were in uniform. Johnson tried to stay out of nightclubs, feeling that the guys overseas would resent his having fun while they were fighting and facing death in far off war zones. He also kept away from the Hollywood Canteen, sensing that servicemen there would not understand a big fellow like him not being in some branch of the military. To compensate, Van made frequent visits to military hospitals but invariably came away from them shaken. Seeing the injured boys there "makes you feel so helpless," he told friends.

Johnson's accident exempted him from service after 1943 but not from 1940-1943, during which many other stars began their service. Jimmy Stewart enlisted in 1941 (after trying to get in for a year but being turned away for not meeting the weight requirement), and Tyrone Power, Clark Gable, and Gene Autry enlisted in 1942. Why didn't Johnson enlist before his accident? 

I can only speculate. A possible reason is that his film career was just starting to take off in the early 1940s and he didn't want to jeopardize it. Johnson made his film debut in 1940; between his debut and A Guy Named Joe in 1943, when he suffered the injuries that kept him out of the war, he made about a dozen films and signed with MGM, making the leap from unnamed extra to an actor with prominent billing (although not yet star billing) and a contract with a major studio. By the time he was reasonably established in Hollywood and might have felt that he could step away from it and have something to return to, he was debilitated by the car crash.

In 1949 Johnson finally served in World War II—virtually speaking— when he appeared in the film Battleground, the first major World War II film to be made after the end of the war. 

Van Johnson as the Minstrel in Batman