Welcome to epic, @folkfan. Every thread has the potential to become like this one has. Many do, for better or for worse.
Length, in and of itself, doesn't make the ski faster. The longer ski's added stability that makes it more comfortable and safer to go faster.
Length provides stability on a flat running ski. Much of the stability comes from greater swing weight which makes the ski less prone to deflection as well as the greater weight overall simply makes the ski better able to maintain whatever direction it is going. In the specific case of DH skis, which have a fairly large turning radius, the large radius helps prevent you from making too small a turn for the high speeds you might attain. If you have gone fast in a straight line on a turny ski then tried to make a turn, you'll know what I mean.
Look at WC racers and their gear. They choose the appropriate length and turn radius (within the rules) for the type of course they are going to run. Faster = longer. Turnier = shorter. Turn radius ratings also mirror the turn size of the course.
Any ski is going to have a set of characteristics that make it more suitable for some functions than others. If your goal is to go fast, go long with a long radius. If you want to make lots of little turns, go short with a small turn radius. You can make practically any ski conform to practically any type of skiing if you are willing to deal with design shortcomings for a particular task. Choosing the right ski for all expected skiing is the challenge. You wouldn't bring your DH's to ski the trees and you wouldn't bring your 5-point powder skis to a DH (except to inspect the course and keep it from snowing )
I'm sure there will be discussion of increased friction due to greater surface area in contact with the snow as well as reduced friction due to less pressure per square inch; you can see where that will go. Probably another 10 pages worth.