Assuming that teaching methods have to be at least partly "Guest Centred", ie based on which experts the learning skiers wish to emulate, the importance of racing to the world of ski instruction will depend to a certain extent on its popularity. This is difficult to measure as a worldwide trend, because it tends to increase in countries that are currently in the ascendancy in World Cup (Austria, USA) and decrease in countries that are going through a lean spell (France, Switzerland, Italy). The greatest threat to racing's popularity is, paradoxically, improvement. Improvements to equipment have reduced the influence of racers' skill, and made races closer. Improvements to course preparation and maintenance (more consistent snowmaking, the "injection bar") have made racing fairer for the whole field, but also closer. When the layman's eye can no longer detect any difference between the best, say, ten racers, the unfolding of the race becomes less dramatic.
As other types of skiing gain media exposure, in theory more recreational skiers will wish to drop off cliffs, ride the halfpipe, or race head-to-head down a skiercross course (some European resorts now have "public" skiercross courses as part of their terrain parks). In practice, the self-preservation instinct will limit participation, but the aspiration will still be there. (Much as the skier taking a lesson in the 1970s wanted to learn the elegance of a Thoeni or a Stenmark, without embracing the risktaking approach of a Klammer.)
The strength of ski-racing will always be its measurability, and the impartiality of the clock. Your time down a racecourse remains the most reliable indication of how successfully you can carve your turns. Freestyle (old & new school) and big-mountain skiing, being judged sports, will always be vulnerable to the type of controversy that hit figure skating at the last Olympics. Of all the new disciplines, skiercross perhaps has the most potential, and could become as popular as traditional racing, if it can solve two problems: making sure that rulings on collisions don't start to dominate the outcomes of races (like already happens in short track speed skating) - and creating courses with enough overtaking areas, to stop a skiercross race becoming basically a starting competition, with an obligatory procession down the course tacked on afterwards.
Enough about what people will want to learn, but what will they need to learn? A mogulfield will perhaps always be, technically, a world unto itself, but carving on piste has grown in popularity since "shaped skis" appeared around '96, as an ever wider ability range of skiers discover the fun sensations of carving. Will the pendulum ever swing back? Logic, and past experience, dictates that eventually it probably will, but there are few signs of it yet - witness Atomic bringing out a "multi-conditions ski", the Metron B5, with a 12-metre radius. Even in the "whipped cream" of off-piste, the width and shape of modern "freeride" skis has enabled more skiers to use more of a carving, and therefore loosely racing-based, technique. Of course, the main question (which I have seen posted in another Epic thread) is: are "normal" skiers' bodies built to withstand the forces generated by modern race-type skis and race technique? And if not, does this mean we merely have to "dilute" modern race technique for mass consumption, or intrinsically alter it?