Teachers aren't the idealized constructs they often use to teach.
That is a completely different issue, classrooms have a specific exception (USC title 17 chapter 1 § 110 (1)) which allows "performance or display of a work by instructors or pupils in the course of face-to-face teaching activities of a nonprofit educational institution, in a classroom or similar place devoted to instruction".
The issue at hand here is that textbook publishers can't (or won't) include the speech or even major excerpts of it. And although a teacher can buy the speech DVD and play it, it's not a very good support to study the speech.
Furthermore, use of the video is much more heavily controlled by the King estate.
The issue is the price not the payment per-se.
We still have Norton's Antologies, right? Many of those are 100% filled with copyrighted works they need to pay royalties on. And they do. And everything works out just fine.
Here is even an illustrated form for children with a CD: http://amzn.com/0375858873
Showing your age? :)