Interesting analogy but the cappa magna was not always crimson nor worn only by cardinals.
Before Paul VI changed the choir dress of prelates cardinals wore the crimson cappa magna along with a violet one in penitential seasons.
Bishops of a diocese wore a violet cappa magna most of the year and a black one during Advent and Lent etc.
Cardinals and bishops of religious orders had their own dress relating to the order to which they belonged.