Assumptions:
The sexes are similar in appearance, and the color change is shown by both sexes, so it is not strictly a mating behavior.
The volume of blood diverted from the facial skin would be a trivial amount, so the rest of the bird would not benefit from its diversion from the face. (So this is not equivalent to more
blood flowing to a human's gut after eating, during digestion).
The sub-epidermal vessels are usually engorged, which is a signal to other caracaras that could mean, "I'm an adult Crested Caracara, and I am not stressed right now."
I doubt that other species of birds or the prey care what color caracara faces are, so presumably it is a signal only between or among individual Crested Caracaras.
When the bird is threatened or stressed, etc, the sub-epidermal vessels constrict, causing the face to become "pumpkin colored" then the "pale," within seconds.
The color change would mean to another caracara, "I'm stressed!"
It seems at first blush not to happen fast enough to be the equivalent of the Blue Jay's scream, "We're
under attack!" or "Let's go get that owl!" But maybe caracaras are very sensitive to even slight color changes, so the signal could occur with the
first shade of color change, right away, when even a few seconds are too long. Maybe a signal that takes a few seconds is quick enough.
Just how would other caracaras react to that silent facial signal and to the raised crest. (I guess the simple answer is a rhetorical question, "How does
any bird respond when it sees that another bird is stressed).
The "I'm stressed" as a signal to other caracaras could mean, "Danger is near."
Or "Not now, I am too stressed."
Or, "Help me!"