Both the Soviet Union and the Nazis took a keen, ideological interest in the production-side innovations of "Fordism," but to my knowledge only the Nazis parroted Henry Ford's statements on the benefits of automobility and made any attempt to promote mass automobile ownership. Why didn't the Soviet Union develop any program similar to the KdF-wagen (Volkswagen)?
Part of it would have been Soviet attitudes towards private property, especially consumer goods. So for example Stephen Kotkin details in "Magnetic Mountain" how Stakhanovite workers and some privileged managers were awarded cars. But the emphasis in state propaganda about this was that this was a reward for hard workers and 'cultured' or modern people. So in a sense automobile ownership was one sign of elite status in Soviet society.
The other aspect is availability and quality. In Chernayshova's "Soviet Consumer Culture in the Brezhnev Era" it emphasises that cars and even fridges and such weresubject to long waiting lists. So even if you could buy a car, you wouldnt just get one. Never mind if the car was something you might like to drive instead of say transport goids in.