And of course Batman had to be a government agent, since everyone in wartime movies had to be a direct supporter of the war effort, and being an extralegal vigilante would've been too subversive.
Batman was also a government agent in the 1966 Adam West movie.
I love the 1943 serial as a strange example of WWII propaganda.
One thing about the 1943 serial that stuck out to me what Batman's undercover gangster alter ego, Chuck White. This especially tickled me when I found out that Chuck White was also the name of the new regional manager at the call center where I used to work.