At $JOB, we have a similar issue with static content. We serve over 1PB a month and the price AWS would charge to use CloudFront is an order of magnitude larger than even a Cloudflare Enterprise plan (which comes with some nice bells and whistles that Cloudfront doesn't offer).
Even with discounts from AWS it just doesn't make sense to use AWS to serve up the assets to users.
We do use S3 as our static asset backend and the combination works really well. I would love to see Cloudflare release a S3 compatible storage service though. I think we'd jump onto that in a heartbeat.