In analog printing color negative film to RA-4 paper, one approach is to project the image to the easel, place a diffuser in the light path, and then place a filter calculator (an array of filters of varying magenta+yellow filtrations) on top of the paper and make a test print. The filtration on the test print closest to gray is supposed to be the correctly color balanced one for the image. How and why does this work? If I take a picture of a red wall, for example, I wouldn't expect the image to average to gray. (Understood that this works MOST not ALL of the time.)
To achieve an equitable color balance, it is necessary to present the paper with a spot-on mix of red, green and blue exposing light energy sourced from the projected image of the negative. If the exposing light mix be biased as to color or intensity, substandard print results.
Now the vast majority of images contain substantial neutral areas, we are talking black, gray and white in varying densities. Should these neutral areas reproduce with a color tint, an observer will declare, the image is off-color. This description being true most images integrate to gray. Integrate means we can laminate a print to a top and spin this affair at high-speed we will be viewing a blurred - gray image. We can also view this grayed integration if we optically scramble this image using diffusion.
Note: If the image is comprised of large areas of strong color, it will not integrate to gray and the method you describe will not yield a satisfactory filter pack. Let me add, the method you describe yields a good start filter pack for the majority of typical negatives. I say good start because every print made will require touch-up filter pack adjustments and exposure adjustments that fine tune resulting print. Also, the principle behind using a gray card target to measure exposure is based on the fact that a typical vista integrates to a battleship gray with about 18% reflectivity.