Magnus makes an interesting point today when he says that he doesn't believe it's possible to teach without influencing style, which is probably very true.
I'm also of the opinion however, that everyone should be able to perform the basic casting stroke as pictured here. In fact I appear to differ from the trend of trying to teach everything style-free and consider the elbow-aligned cast to be a "foundation" cast, and very possibly without style.
Yes you can put a rod in a pupil's hand and say, "here's a bunch of stuff to play with, all we really want is nice loops, you can cast anyway you want, but you'll have to work it out for yourself first". But why? Every half-decent caster I know, whether or not they are noted for a particular style, can all throw a straight loop with the elbow in-line to the target. I consider that to be an essential cast that everyone should know.
So I'm of the opinion that you should attempt to teach this classic foundation stroke first and then allow them to discover "style". And if you want to start with the Oval Cast as a foundation then that works too.