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It would require the DB601 engine, of which there were already too few to go around, so that's a major problem unless it adopts the Jumo 211, which was bigger and not up to the type of performance that the Daimler's gave.
Messerschmitt, Focke Wulf and Heinkel all preferred Daimler-Benz engines for their fighter aircraft designs. It stands to reason DB engines must have been superior for that role even if they look similar on paper.
The Jumo 211 was in short supply and/or lacked power in 39/40, otherwise they would have not used the DB 601 in the He 111 P-series (of which 834 were built).
Nazi foreign policy was not that rational. Germany was hardly going to empower nations on whose territory it had other designs.
Cheers
Steve
Germany was most certainly not going to empower a country inhabited by people who they were planning on enslaving!