The story I hear is that it was either Louis B. Mayer’s or John Ford’s threat that if Wayne enlisted for WWII he would never work for either studio again. They also convinced him that making war hero movies would be of greater service to the allied military effort than being one of hundreds of thousands of soldiers.
Perhaps that’s why he didn’t talk about it much; many patriots would have dismissed that as a lame excuse. I don’t, since we won the war.