I honestly believe it all depends on 1. how many days a season you ski, 2. where you ski (are you confined to one area or do you travel a ton), and 3. whether or not you are in the snow sports industry.
For me, I could get by with 3 skis: 1 for teaching, 1 for every day free skiing away from work, 1 for powder. But then I also enjoy backcountry skiing, so that can potentially add another stick to the quiver.
If I found the perfect ski for Tahoe/Colorado/Utah/Wyoming that I could teach on, rip groomers on, surf the powder, bust the crud, and take for 6+ hour tours, that would be awesome and I'd only need 1.
That said, I'm pretty content with a 4 ski quiver: teach ski in a short length with a medium short radius; every day ski for days off; powder ski; A/T ski.
Given that, though, I spent most of this season on 2 skis only: 180 cm Blizzard Titan 9 as my teach/every day free ski and 185 Volant Spatula for my powder ski. I've pretty much made do with that 2-quiver set-up for the past 2 seasons and it's worked pretty well. I break out an AK King Salmon for my A/T set-up in the spring/summer, so it's a wishy-washy 3-ski quiver, but that will probably change come next season (may be jumping to a 5 ski quiver: teach, every day, powder, mid-fat A/T, powder A/T).
Again, I really think it depends heavily on where you ski and how much you ski.
Then again, having worked with some kick-ass ski instructors this past season (many of whom have been on various local, divisional, national, and international demo teams), I've seen folks who only have 1 pair of skis and they kill it in every condition, every type of terrain.
so in all honesty, if you're a really good skier, you should really only need 1 ski....having multiple skis is really a luxury and in many instances just fun (but for some it's also an addiction and for others it's the age old story of the carpenter blaming his/her tools for his/her technical shortcomings).
After all my rambling, I can say that I could reasonably get by with a 2-ski quiver: one for teaching and one for powder, but I would have to choose the teaching ski so that it could also be my every day freeskiing ski and my A/T ski, which might be a tough match to fit.
My total bad!
I failed to answer the original question:
The benefits of a 1-ski quiver would be the following:
1. less money spent (i.e. by purchasing 1 ski you would have more money to throw around on lift tickets, travel, other gear, etc.)
2. less maintenance (and again less money spent as you wouldn't be tuning, waxing, and repairing multiple pairs of skis)
3. less clutter (it takes some room to store multiple pairs of skis)
4. having only 1 ski would make traveling so much easier (and again, take a look at #1 above)
5. you would become the master of that 1 ski and conceivably improve your technique by focusing on your skills on that 1 particular ski (i.e. there is something to be said about sticking to one product and really learning how it works and mastering it. If you aren't a terribly strong skier or you don't ski more than, say, 60 days a season, continually switching skis could be a detriment to your improvement on the hill; as MTT once said to me "Pick a ski and make it your b#$ch": in other words, it's wise to pick a ski that fits your skill level, master it and improve your technique before you start getting multiple pairs of skis that you may or may not be able to handle).