I was wondering the same thing. Possibly not as prominently visible as in the little videogame recreation, possibly somewhere only Roscoe 'Eagle Eye' Brown was likely to spot it.
Because to do otherwise is a violation of the rules of war.
There were a number of Allied aircraft that crashed (or occasionally landed by mistake) in Axis territory in flyable condition. All of them were repainted with Balkenkreuze or whatever the Italian Fascist symbol was called for testing purposes, and some of them were used for reconnaissance.
In Italy, a captured P-38 was actually used to sneak into formations and shoot bombers point blank, but that only worked once or twice before the Americans caught on and the Italian ammunition jammed the P-38s' guns.
Also, a lot of Axis planes ended up in Allied hands, particularly Ju-88s accidentally landing at English airfields, and were similarly repainted, but as far as I know they weren't used for sneakery.
B-17s and B-24s were captured and used to infiltrate US formations long enough to radio their position. Bomber gunners got real trigger happy when they found out, and stopped accepting unknown stragglers.
Here's a question. Why aren't I watching 100 blaxploitation films about Roscoe C. Brown, fighter ace, Nazi-killer, and accidental two-fisted counter-intelligence agent? I'll tell you why. Because there is no god.