The intersection of that and communication skills is rarer, but it happens often enough, especially for people who pick up a second major in the humanities or did a lot of public speaking prior to/during college. Again, not the average case, but not terribly uncommon.
I think we may differ on what we mean by "should". I don't (really) doubt that it's possible and valuable to learn all of this in university (forgive my use of hyperbole in the original comment). But I don't think it's necessary for most people with a major/master's degree in CS to do so.
The ideal and the necessary should not be confused.