Regarding your second two points, the idea of signalling games is that as long as C has some influence on your behavior, others can deduce from your apparent trustworthiness, altruism, etc., that you are at least somewhat trustworthy, etc. If you did away with C and simply made your U more trustworthy, you would seem less trustworthy than someone with a C, and other agents in the signalling game would assume that you have a C, but your U is unusually untrustworthy. So there's an incentive to be partially hypocritical.