@johnnycamp5, here are four reasons why I think the spectral balance of the reflections should be similar to the spectral balance of the direct sound:
1. Timbre is more natural when the reflections fully support the first-arrival sound. Where the reflections are spectrally different from the first-arrival sound, they can skew the perceived timbre towards that difference. Also a rich and spectrally-correct reflection field inherently supports good timbre (as long as it decays neither too quickly nor too slowly), as is demonstrated by the acoustics of a good recital hall or concert hall.
2. If there is a significant spectral discrepancy between the first-arrival sound and the reflections, the ear/brain system has to work harder to correct identify the reflections. This is because the ear/brain system looks at the harmonic structure of all incoming sounds to determine whether they are reflections or new sounds. The more the overtones in a reflection differ from those in the direct sound, the harder the ear/brain system has to work to correctly classify them as reflections, and over time the additional "CPU usage" can result in listening fatigue.
3. The effective in-room signal-to-noise ratio can be degraded if the overtones in the reflections become inaudible before the rest of the spectrum does. (This can also be caused by excessive in-room absorption attenuating the short wavelengths moreso than the longer ones.) Once the overtones in the decaying reflections have become too weak for the ear/brain system to recognize them as reflections, they cease to be "signal" and become "noise". The net result is a raising of the effective in-room noise floor and a corresponding reduction in dynamic contrast and liveliness.
4. Reflections are the carriers for the reverberation tails on the recording, which in turn convey the venue ambience. If the overtones in the reflections are too weak, the venue acoustics are no longer effectively presented and the "small room signature" of the playback room is more likely to be perceptually dominant.
@soix, I don’t think kenjit has raised a legitimate issue so I won’t waste everyone’s time by replying.