My Canon has extra saturated reds so that may contribute to the problems with reds. I find that both red and black "swallow" the curves and accents of a car where white or silver really show them off. So special or extra lighting effort is needed to get either illumination or shadows onto the surfaces necessary to highlight a curve/edge/crease. Circular Polarizer?
The example you have of the red car seems to have been shot at the height of the daytime and possibly without a polarizer.
I applied a super quick neutral gradient filter that shows the image does contain the data so you could always do it in post-processing: bring out the shadows and tonal contrasts. I only spent about 40 seconds so there is not a lot of effort in blending/smoothing or getting the amounts of tonal adjustments optimized.