I was always required to take a full range of subjects, from math to lit to a full range of science classes, along with history, government and technical drawing.
My undergrad degree was Phi Betta Kappa, which requires excellence* in the liberal arts and sciences. My grad top degree was Phi Kappa Phi - which is outstanding work in one field, and that seems right to me.
Most of the people I work with have an outstanding degree of technical competence in carpentry, mechanics and electricity, but they are also (for the most part) extremely literate in cultural stuff and can go on for hours about music, theater, opera and all that stuff. They can read (and execute) schematics and blueprints, you can trust them with professional power tools, and they can quote Shakespeare at length also. Oh yeah, they are also very, very good with people. Hell my vitia/resume says under special skills: Works well with difficult people, works extremely well with extremely difficult people. And that's true.
The classic quote comes from Heinlein speaking as Lazarus Long:
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly.
Specialization is for insects.
* - That's academic speak for all 'A's.