I think it was a lot more complicated than your comments indicate, just look at the number of projects compared to RLM designations. Arado alone numbers in the hundreds as does B&V, etc. In some instances designs were a response to RLM requirements. Many more designs were probably the results of applying aerodynamic, powerplant, weaponry, structural, and other developments to improve performance and mission capabilities resulting in paper studies. There are still many gaps in the known sequence and to my knowledge none of the primary documents summarizing these assignments (which surely must have existed at one time) have come to light. One last comment, the scope of the RLM was much greater than it’s contemporaries in the USA and GB, it was a combination of NACA, Air Force and Navy procurement, industry planning board plus the airlines and CAA. Much of the financing of the German aircraft industry was received from the government, so the RLM had a considerable oversight in day to day operations. Private ventures were as a result , the exception not the rule. IIRC, there were some company developed designs that ultimately received RLM 8-nummer assignments and ultimately hardware, but these were the exceptions
Best Regards,
Artie Bob