Can you elaborate on your definition of compression please?Compression is a much bigger problem than most designers will acknowledge. It happens at surprisingly low SPL, especially with lower sensitivity drivers and lossy crossovers.
Crossovers have a big impact on dispersion pattern of the drivers. Ever heard of lobbing?
I agree that compression and radiation pattern will both impact believability significantly and harmonic distortion from the speaker not so much. Earl Geddes did not think that harmonic distortion of compression drivers had any significant impact on perceived sound quality. He felt the horn itself was a much bigger barrier, which is why he came up with his oblate spheroid waveguide/horn to prevent HOMs (High order modes) that cause problems in a lot of other horn types.