What is the reason that some departments do not allow PhD students to be instructors of record?
My institution (which is a highly ranked R1 private university) tries to differentiate itself from other universities by advertising that all of our professors teach  and that the undergraduates -- if they choose to come here -- will learn directly at the feet of the greatest scholars in the world (blah blah blah..). 

My cynical quip aside, we try very hard at least nominally to ensure this. All professors in the arts and sciences teach their own classes (research staff at the medical school are of course exempt), although some teach less than others. 

Very few graduate students are permitted to be instructors of record -- only just a handful of 6th and 7th years are given this right, and only in very focused seminars.

For us, it's a bit of a matter of pride -- what differentiates us from some of the other R1s. But like most things in the neoliberal academy, there has been talk of bringing in adjunct faculty and other changes that will certainly dilute the claim made in the opening paragraph above.