All of the Jumo 004's problems had nothing to do with the compressor. The Germans were forced to save alloying additives (nickel, first of all), as a result, the heat resistance of materials for the hot part of the engine was insufficient. The limiting factor was the combustion chambers, the next was the turbine blades - even hollow air-cooled turbine blades did not provide the required material durability. If the Germans had enough skilled workers to produce the hot part of the engine from suitable materials, the reliability of their engines would not differ from that of the British. Under nickel shortage conditions, the Germans could use any type of compressor with exactly the same result. German engineers chose the most promising type of compressor and created quite good engines, as the further development of jet engines showed. The centrifugal compressor was a temporary dead-end solution.
Except it had nothing to do with the compressor.
