Well you evidently know what your talking about. Do you know why the Hellcat, Corsair and P47 would all have such different props when they are all large, heavy fighters, all 3 have the same basic engine and all 3 started out with 2000 hp? I can't see why all 3 wouldn't have the same prop.
You might also notice that all three types have different super/turbocharging ratios and different FTH altitudes despite having the same basic power plant.
A different prop is required to meet design needs..
I know that the same exact fighter types also used different props. Some props favor top speed, while others favor climb, and others favor acceleration, particularly in a certain speed range. It just depends on the use of the fighter, long range escort vs interceptor.
The chord of the blade and width will maximize performance where its needed.
Tip speed was also an increasing concern as fighters developed. They began squaring off the tips of the blades to help control mach effects.
You might also notice German designs have a thicker chord toward the center of the blade, almost triangular in shape this was also said to help control mach effects.
I think understanding the propeller type is as important as understanding the power chart of the engine.
It gives a better picture of how engine power actually translates into thrust.