From the individual intellectual point of view it's better to have a better education, but from the collective point of view having too many wild cards is not good for anyone. If there are too many physicists, they won't earn enough to justify the cost of the studies, and won't be happy in a menial job after spending years learning advanced mathematics.
If anybody can do everything interchangeably, it also tends to create a monoculture which is a more fragile system.
Often it's better not knowing how the sausage is made, and trusting that people who have specialized know what they are doing.
Wild cats ("overeducated population") are dangerous.