When all, or most all combatant's air forces had 'roundels' on both the upper and lower sides of the wings, the US had only one 'roundel' on the top side of the left wing and one on the bottom side of the right wing. Did we run out of 'roundels', or were we just conserving them'?
We were probably looking for a way to further distinguish US aircraft specifically from other Allies - round is just round when, as they say, "you're operating on brain-stem only"...
...I could think of another reason, too. Like that typically people tend not to scan to their right side first (at least people that grow up driving on the right hand side of the road have this generalized habit...). So if you're sneaking up on someone from behind you'd tactically prefer to do it from their right side.
Not having an ID mark on the upper right hand wing might force an opponent to have to get closer to make the ID in order to take a shot - giving the defender more time to scan that part of the sky and be able to defend/avoid.
Actually willshak pretty much answered his own question, although "conserving" was probably not exactly the right word.
It's little-known fact that from early 1942 right through to the end of 1944 there was an unbelieveable shortage of stars in the U.S.A., hence putting said stars on only the one wing.
Contributing mightily to that shortage was someone's ill-advised requirement that stars (within a circle) be placed on all wheeled or tracked vehicles. It became somewhat alleviated when the requirement for the circle around the star was dropped - although the stars themselves were still in extremely short supply.
In looking at old black & white photos and films of the WW II era, one can immediately notice that all U.S. flags were only allocated forty- eight stars - again an indication of the shortage of stars. Post-war research indicated that putting only forty-eight stars on each flag allowed for an additional 48,715 flags to be deployed.
And now back to my extensive research library.....
and don't forget all the stars who were working for the war effort and were unable to make movies or do appearances. some flew, some were in the navy and some sold bonds. they certainly couldn't be on airplanes.