The Ivy League and the US Cabinet

I'm looking at the current Cabinet. I'll note President Barack Obama, Columbia (B.A.) and Harvard (J.D.), adds to the count.

Vice President -
Joe Biden: University of Delaware (B.A). Syracuse (J.D.)

Secretary of State -
John Kerry: Yale (B.A.), Boston College (J.D.)

Secretary of Treasury -
Jack Lew: Harvard (B.A.), Georgetown (J.D.)

Secretary of Defense -
Ashton Carter: Yale (B.A.), Oxford (PhD)

Attorney General -
Loretta Lynch: Harvard (B.A. + J.D.)

Secretary of Interior -
Sally Jewell: University of Washington

Secretary of Agriculture -
Tom Vilsack: Hamilton College (B.A), Albany Law School (J.D.)

Secretary of Commerce -
Penny Pritzker: Harvard (B.A.), Stanford (J.D. + MBA)

Secretary of Labor -
Thomas Perez: Brown (B.A.), Harvard (M.P.P. + J.D.)

Secretary of Health and Human Services -
Sylvia Mathews Burwell: Harvard (B.A.), Oxford 

Secretary of Housing & Urban Development 
Julian Castro: Stanford (B.A.), Harvard (J.D.)

Secretary of Transportation -
Anthony Foxx: Davidson (B.A.), NYU (J.D.)

Secretary of Energy -
Ernest Moriz: Boston College (B.S.), Stanford (PhD)

Secretary of Education -
Arne Duncan: Harvard (B.A.)

Secretary of Veteran of Affairs -
Robert McDonald: West Point (B.S.), Utah (J.D.)

Secretary of Homeland Security -
Jeh Johnson: Morehouse (B.A.), Columbia (J.D.)

That's ten (10) out of 16 positions that currently have at least one Ivy degree. The last non-Ivy League president of was Ronald Reagan who graduated from Eureka College (B.A.). As respectable as Eureka is, it's not Stanford. What's even more strange is that six positions are the only ones that don't have a person holding J.D. acting as head. Why are there so many juris doctors, whose resumes barely even make them qualified for such positions, managing these departments? Want to be in the Cabinet? Get a law degree. Want a political career? Get a law degree.

Let's tally.

Harvard - seven (7)
Yale - two (2)
Brown - one (1)
Columbia - one (1)

Non-Ivy Elites: Stanford - three (3); Georgetown - one (1)

You also have two Rhodes Scholars in Carter and Burwell.