If the signal to corporations disappears the wage premium to a college education disappears and the students disappear along with the tuition paying the professors’ salaries.
The credential was certainly something - a more easily understood distillation of the of connections and status that got you there. But that's not exactly professional the way a degree in Business is.
Besides, were there not other high-minded notions that underpinned that credential - ideas of self-development and virtuous leadership? And more crass notions of polish and status? Were these not the self-justifications of these elites, made manifest through the institutions?
As a side note - I do strongly suspect elite schools will bring these ideas back. If not for virtue, for necessity - as schools seek to self-justify in ways that go beyond the dollars they risk losing.