500 years ago literacy commanded a substantial "skills premium" on earnings relative to the larger illiterate population. Today most people in the work force are literate and literacy is not a distinguishing quality for higher earnings. But on a societal level, I don't think that developed nations could be as prosperous as they are today if literacy were as uncommon now as it was 500 years ago.
To relate this to your bachelor's degree example, if everyone earned a bachelor's degree in e.g. physics then the earnings premium for STEM graduates would drop if not vanish. But I expect that society's collective material prosperity would increase. I say "earned" rather than "got mailed a certificate" because getting a certificate without developing the corresponding abilities is not useful.