It's not pointless because now you know what has to be done to get the results you want. It isn't a matter of color balance when you take the shot, and the lighting you used for that shot was just fine.

If, and only if, you are using the JPEG straight from the camera as opposed to working with the RAW file, you can change the camera setting for more saturation and higher contrast. It might well be possible to come up with a camera configuration that nails it, and then it would just a matter of using the same setup for every shot.

Here is an example of what can be done with that image as captured. The essential editing was to reduce the brightness and then increase the contrast. That can be done in more that one way though. I tried brightness and contrast sliders and decided I wanted finer tonal control, so I backed out of that and used a curves tool to do exactly the same thing except it allows adjusting the slope of the gamma curve at different tonal levels.

Note that increasing brightness brings the colored areas closer to the white point, the saturation goes down, and it looks more pastel. But by decreasing brightness the opposite happens. Then if contrast is increased only brightest areas are brought back up to near the white point, allowing the paper to look white while the colors are not washed out.

I did adjust color balance very slightly, by raising the red 12 points. That has no effect of saturation or brightness though.