Watch a slalom racer. Their skis are not always on the snow doing "bendy" turns. At the critical high energy parts of the run, their skis are doing most of the turn in the air. The energy for that turn has to come all from the skier. A lighter ski in the air will be able to turn faster, later and more than a heavy ski. Once the skier gets used to that, it could be an advantage.
Bump skis move extremely fast. Up and down, side to side as well as twisting. The skier inputs are a huge part of that motion. Light skis really rock the bumps.
For me, powder and crud are all about balance. If I'm balanced in my core, it feels right. Extra mass way away from my core (heavy skis) is destabilizing. Especially if I have to avoid a tree with a forced quick turn. Personally, light skis matter most in powder and crud for my skiing.
@KingGrump There's always a flat runout back to the lift. Skating with light skis is so much easier.
I'm old enough that riding up the lift with heavy skis hurts my knees. I'm not alone - have you seen some of the weird devices and straps people use on the lifts?
Even if you don't hike much, you still have to carry skis to the lift. Light is magic there.
While the best ice skis I've ridden were super heavy Bode Miller Head SL Racers, the Slant skis were almost as fun on a nasty icy day. Fresh tune (Sierra Snow Labs both builds the skis and does awesome tunes) of a fairly light all mountain ski surprised me at how quick and lively a ski could be while offering an edge I could trust.
@markojp is right, weight is just one factor in ski performance.
The light car is a lot easier than the heavy car to pull out when they get stuck. Having a place several miles in on a dirt road, I know this firsthand.
Eric