The thing is to give beginners a simple motion for a basic cast.. They are not going to cast 60 feet as beginners. So the foundation cast is just that, a foundation. It is to learn a simple cast and to get the muscle memory to feel the rod bend.
Many techniques work. What I am saying is that this technique is simple and easy for beginners to learn. To say that you can use other motions like Lefty Kreh's low elbow technique is beside the point. Or you can use the elbow up to the side technique of Dan Blanton and Bruce Richards.
This simple "elbow forward" technique is the one that Joanne Wulff, Mel Krieger, Gary and Jason Borger, Jim Green, Jerry Seim, Steve and Jeff Rajeff use. It is basically the technique developed at the Golden Gate Casting Club.
As you lengthen the cast, you can open up your arms and use a fuller casting motion. But to teach this full arm technique to beginners creates a greater opportunity for casting errors.
To explain the various casting styles, Al Kyte wrote the article below. Using any of these style, you can cast well. However, you will note that most of the casters that are known for instruction favor the elbow forward style. I think it is because it is the easiest for beginners to grasp.
As to whether it is 10 to 2 or 11 to 2 or 10 to 1 for a perfect cast is really irrelevant. As Chris said, as the cast lengthens, the angle can widen. If we are talking about what to tell beginners, I maintain that if you tell beginners 10 to 2, you will often get 9 to 3 or 9 to 2 or 10 to 4, etc, etc. It is MUCH easier to get then to OPEN up the angle than to tighten it. Their instinct is to wave the arm and break the wrist!
So start them with shorter casts and smaller angles. You want them to have success early with a relatively tight loop. Then they can lengthen and open that casting angle.