I have been an Austrian trained ski instructor since 2012 and I can tell you that a sharp ski is essential if you want to have carve in any conditions below where the snow isn't slushing or soft. I.e. any run that is either early day, windblown, mid-season (generally colder) or shadow side.
HOWEVER 99% of the skiers on a mountain (and yes I mean 99%) do not actually ski on their edges, they do skidded turns (https://www.youtube.com/watch?v=S4hioJ4ThJA). And the same 99% will typically just slide off of hard and icy parts of a slope as they aren't comfortably riding their edge. To these people sharp edges matter, but less than to the few who successfully carve.
But if you are within that 1% of skiers that do ski mostly on the edge, then a sharp edge is extremely important; you see true carving technique is a delicate skill:
In order to carve properly you need to need to get your skis in a steep angle with the snow, which means you need to get your feet in a steep angle, which can only be maintained if you move your center of gravity into a position that isn't above your feet. Which effectively means your body is in a position that is out of balance. Similarly to how sprinting essentially is just leaning forwards and playing "catch up" with our legs, carving technique tries to do the same. Exception being that we use the rhythmical centripetal forces of turns and the resistance of the snow to create the balancing force (https://d3t7modobimpp4.cloudfront.net/uploads/_1200xAUTO_fit...).
And this is why edges matter; because if the centripetal force provided from the carving turn isn't generated because the skis blunt edges cause them to slip, then instead of generating movement towards the skiers body (reestablishing balance), the skis will drift away from the skiers body (removing balance) resulting in poor turns if not slipping down onto ones hip.
TL;DR:
Very good skiers NEED sharp edges to ski well. Most skiers will be fine.
(As a matter of fact I think 99% of all skiers will do just fine on ANY ski, and make more significant improvement from 2 days of ski school than any equipment upgrade or tuning that money can buy).