I agree with you, Arc! Skiing skills are the essential foundation for becoming a better racer. Time in gates is important too, but without the ability to make a good turn, there is an absolute wall you will hit--like the self-taught golfer who reaches a frustrating plateau.
I have seen skiers with seriously deficient skills become REASONABLY fast in NASTAR-type courses, though, just by spending countless hours there. But again, they always plateau well beneath their potential, until they focus effectively and spend some time on the fundamentals of good technique.
Good ski instructors--even those who spend little time in gates--understand, demonstrate, and teach the very same fundamental movements that make skiers fast in a race course. As I've often said, "good skiing" is "skiing a slow enough line as fast as you can." The "slow enough line" part is a tactical choice that allows you focus on gliding, "offensive" movements without needing to use your skis as brakes. The "fast as you can" part is what allows you to ski ANY line faster!
Good instructors, of course, are capable of teaching all kinds of movements suitable for all kinds of intents and tactical situations. But that includes--especially--the gliding, precise, efficient line-control movements of racers!
Because race gates don't hurt as much as aspen trees or snowboarders when you hit them, the exact line you might take through a race course is a LITTLE different than the line you might take while free-skiing through obstacles. There are some "race-specific" tactics that can only be learned in a race course. So both time out of the course, developing better technique, and time IN the course, developing better tactics--both under the watchful eye of a good coach/instructor--are important if you really want to reach your potential as a racer.