I think your math is off. There is a minimum of 11 and maximum of 13.
Social Science (2)
Quantitative Reasoning (2)
Foreign Language (1-3) Depending on what level you place into.
Of the 9 courses my son has taken so far, he has yet to take one not taught by a professor.
Are the graduate student teachers so bad that they are undesirable?
Well there are no "graduate student teachers" for 99% of classes. Every class I've had has been taught by a professor (one was a postdoc I suppose). What you do have is discussion sections where 18 kids from your class get together and talk about the material for an hour, and those are led by grad students, but those are like an extra class for any given course, and not a standalone course. I think some of the intro calc courses are taught by graduate teaching fellows, but pretty much every other class is taught by a real professor.
Thanks for the replies. I believe that a professor would be in a position to broaden students' views for distributed courses as recommended by Kdog in another thread.
Here's a few examples of classes you could take:
HSAR 115 Introduction to the History of Art: Renaissance to the Present
ANTH 172 Great Hoaxes and Fantasies in Archaeology
PHIL 181 Philosophy and the Science of Human Nature
PSYC 171 Sex, Evolution, and Human Nature
I think some foreign language instruction classes are taught by "instructors" or perhaps grad students. When I was a student at Yale (30 years ago), I had three classes taught by grad students: one was a section of intro calculus (terrible teacher), one was French (good teacher), and one was a higher-level English seminar on Wallace Stevens--I believe the grad student got to teach this by competing for it, but I'm not sure--he was pretty good. And, as noted above, I had grad students for discussion section leaders--generally, they were helpful, but the professor did the actual teaching.
I've had all professors with a couple postdocs - one as a DS section leader/professor (who was OK), and one as a French instructor (who was fantastic). One political science course I took had a grad student TA, but yeah, the instruction was in lecture by a full professor.
Note: that awful math grad student I had as an instructor at Yale is now an associate professor at a flagship state university. Perhaps he's a better teacher by now. The French instructor is now a professor at Hunter College.
Also, my memory was faulty--the Stevens seminar was taught by a very junior assistant prof.
To answer another part of your question: I'm not sure how much information that I've gotten out of my distribution courses I will actually use in my life, ever. But being forced to think about the world from a different perspective than the one my discipline usually takes was extremely useful for me as a thinker, and a good way to keep myself sane when postmodern theorists almost took over my life. I'm glad the distribution requirements exist, however much I complained about them while I was doing problem sets.