Well, it would only work for downloads, not images. And it would require dynamic sites, so static sites couldn't take advantage of it. And it would require some coding ability as opposed to just knowing how to upload a file and point to it. So, it would mean expending additional resources programming-wise just to keep files moving instead of doing whatever actual service we're really working on, since we don't have money to throw at it. And it would increase the load on the website server, too, which would require additional resources, which means more money.
For images, the whole point of a CDN is to keep them in one place with a long expiry (a week or more) possibly downloaded from a nice geographically close edge node so that visitors load the images very quickly once and then cache them for the next pages and later visits of the site. The only current way CDNs implement of keeping folks from leeching/hotlinking images is to check referrals. The unique download link bit would negate the whole benefit of the CDN (you'd lose caching and the back and forth to generate the unique URL would slow it down), so that's out. Basically, lots of folks would ditch CDNs and host internally, possibly using server log checking to see if said IP recently hit a page. Otherwise they have to deal with lots of bandwidth leeches. The end result would be slowing down visitors' experience.
So, for both images and downloads, users wind up losing if referrals go away. It's far better to just leave it as is. Enable referrals by default. Let the privacy conscious disable them (sending blank ones). And build systems to take into account both userbases. Again, as a software developer, publisher, and host, I don't really care about referrals in terms of violating privacy, so I don't care if you disable them and send blank ones. I purposely set up my redirects and CDNs to allow for that. I care about them in terms of continuing to deliver services effectively to my users without competitors stealing my resources.