Recreational skiers can learn a ton of things from racers.
My background and bias: I was an advanced/intermediate skier, skiing 15 days a year as an adult, at a plateau, and then my brother and I got into recreational racing. For the last 10 years, I've gotten faster every year, steadily advancing from 36th to 1st ranking in my state for my age category in NASTAR, going from 25th, to 18th to 12th at the NASTAR nationals (recreational division) over the last three years and working my way up from a below class 6 club racer to advance steadily into faster classes of club racing.
I still have a lot to learn from racing (I hope to continue to get faster and to be able to compete at the Masters level in my 50s and 60s.)
Here's some of what I've learned so far:
1. Conditioning skills. I do balance training, strength training, lactate threshold training and plyometrics. Every year, I learn a little better how to get in shape for ski season. (I live at sea level, and ski against people who have a lot more time on the mountain, so I have to be in better shape.)
2. Carving skills. No matter how good you think you are, skiing in the gates makes you better, because of the instant feedback: The stopwatch doesn't lie. Your line in the slalom gates doesn't lie. The closer you get to a pure carved turn, the more speed you carry.
3. Getting forward. A thousand instructors can tell you a thousand times how getting your weight forward early in the turn bends the front shovel of the ski to take advantage of the reverse camber. But not until you get it by trying it in slalom gates on today's short slalom skis does it really hit home. (How you finally get there might be different: "Let the front boot cuff hold you up" "elbows forward, not hands forward" or "pull your inside foot back at turn initiation." But your skiing gets better when you do get it, or when you mostly get it...)
4. Two footed skiing.
5. How to care for your skis and how to understand their interaction with the snow. I sharpen my edges and wax my skis after every day's use, while 97% of recreational skiers (aaiiee!) never wax their skis at all. Along the way, you necessarily learn a lot about gliding and interaction with the snow, just in understanding why you use different waxes for different temperatures and humidities, and that in turn leads you to think a lot about how you have to change your technique in different conditions.
6. A survival bag of tricks. I'm not afraid of ice any more. (For racers, ice is our friend. It holds up well even if you have a high bib number.) And I've learned a lot of things most people don't think about: how to self-arrest on a GS gate when I'm getting late, how to adjust my line to get back on line over the next two turns, how to punch the snow to bounce back up and avoid boot out.
7. Every year getting a little closer to the form of the World Cup skiers, with hips low, and those extreme angles while still making those turns.