I've stayed well away from this thread for a long time as debating on the internet when there is no actually debate being offered is well...not fun or productive. The second anyone thinks any sport longer then the shot-put or discus in duration and certainly any sport as complex as alpine skiing does not require exceptional aerobic metabolism to perform at the elite level I fear for not only their level of education but would have concern about whether they should be working with athletes at all.
Anyway, there was a request asking for peer-reviewed research showing the huge contribution from Aerobic energy production in Alpine skiing. It took me 3.4 sec to get you these!
This one http://www.ncbi.nlm.nih.gov/pubmed/692307 is a great read, old, but very valid. and states as I and any coach involved in skill heavy sports that "The results suggest more pronounced involvement of aerobic energy metabolism in skilled skiers than in unskilled skiers".
The word "suggests must be approached with caution as it's not definitive but as I said any good coach involved in elite sport that is heavily skill depending and requires multiple training runs/practice etc.. knows not only from research but anecdotal observation that the more skilled an athlete is the less they use their easily "fatigue-able" fast twitch fibers, the more aerobic metabolism they use in general and thus the greater their "anaerobic reserve" is to up a gear and hammer for the "killer punch" when needed.
Anyway that's peer-reviewed study number one citied!
Study number 2! - http://www.ncbi.nlm.nih.gov/pubmed/7752855. One quote says it alll! -
"The giant slalom probably calls for the largest reliance upon aerobic energy metabolism and oxygen uptake may increase to 75%-100% of maximal aerobic power."
The bottom line is the more elite a GS or alpine skier is the greater the contribution from Aerobic energy metabolism in competition and training and as such the greater their anaerobic reserve will be for that killer punch or punches (think Ligety's stivot 2nd run Schaldming World's 2014). An elite alpine skier needs to train all energy systems across their full range of power to capacity. That's Anaerobic PCr and Glycolytic and Aerobic. How an athlete or their coach plans/periodises this training is totally up to them based on the training age of the athlete, individual differences, travel, training and race schedule etc.... but I can ASSURE one thing training an aerobic base and then forgetting about all aerobic training of any intensity for months on end is not the way to ultimate health or performance.
Funny @iriponsnow quoted some research of Block Periodisation of HIIT for skiers, Block method will always have individuals maintaining aerobic metabolism over a wide variety of intensity during accumulation blocks in none power sports - and if you were for a second to speak to Verkoshansky or Issurin and tell them that an alpine skier skiing two 1min+ runs in a day is in an Anaerobic dominate sport they'd laugh!
I will not "fight" over this subject - GS is a complex event involving energy production from all sources, the less skilled you are the more anaerobic it is, the better you are the more aerobic dominate it will be and hence why Ligety, Pinturault, Hirshcer, Kristofferson, etc... make less mistakes or recover faster when they do.
As I said long ago, it's never either or, train all systems, planning of that training is up to the coach and athlete but Strength is the "king" foundation, followed by aerobic power/capabilities then reactive/explosive power only when those qualities are developed to their max should one worry about improving anaerobic glycolytic capacity!