No, it’s not the case that mixing equal portions of red pigment and white pigment gets you a color that is perceptually mid-way between the red and white. You might get something that looks “closer” to the red or looks closer to the white. I actually have talked about this with quite a few artists. Josef Albers (abstract expressionist painter) wrote a whole book on this topic, and other non-linearities in color perception. Personally, I did my PhD thesis on the neuroscience of color perception.

Averaging in a “perceptual” color space doesn’t really make sense because perceptual color is non-Riemannian (source)