I find it odd that one's exposure to and encouraging of bigger-thinking is somewhat reserved until the PhD level and that, after a long while of not exposing or encouraging such, our systems had ever expected people to suddenly think big once at the PhD level. It may be more productive to have the expectation of bigger-thinking introduced earlier and let that expectation be realized more fully at the PhD level.
By the time you're getting your PhD, the college graduate should have read the classics, done at least 1st year level calculus, biology, physics, ethics, philosophy, and 2-4 years of a foreign language.
High school and undergraduate is the time to be broad-minded. PhD is for very focused work (with the big picture in mind).
Personally, I read the classics and learned Greek and Latin (high school), then in college took 8 courses of philosophy, 2 of Spanish, 2 in economics, 4 in business/entrepreneurship, and a smattering of other interesting things (art, music, etc...) while getting a Physics major.
Then I went and spent 6 years learning more about one thing than anyone in the world.