The Luftwaffe was abolished in 1945 and wasn't reformed until the 1960s, when they got these. In retrospect it might have been better if they'd worked up to the F-104.
But it was a dangerous plane for Americans, too, with one of the highest accident rates of any jet. The great Chuck Yeager was severely burned and lost two fingertips ejecting from an F-104 after he lost control.
It turned out that the high accident rate in Germany - much higher than in Japan and other nations - was in part the result of sabotage.
It was one of the few incidences of proven sabotage during the Cold War.