Provide Access to CDN Storage
Currently there seems to be no way to access the storage the CDN is using.
I would like to use Function App with a NodeJS Blob Trigger to minify any CSS and JS files that land up on the CDN Storage.
Another scenario is to jslint & css lint any js and css files that gets stored in CDN storage and send notifications if there's anything that won't lint.
Yet another scenario is to use a blob trigger blobs and optimize any images that gets stored.

There currently isn’t any way to access storage that is used by the CDN for caching purposes. Content is never permanently stored in the CDN cache. By default content is stored for a max of 7 days. Longer or shorter times for this TTL can also be specified. However, in all cases this is just a max value and content can be removed from the CDN’s cache if it isn’t being actively accessed.
Long term we are investigating the ability to have the CDN automatically optimized images and reduce the size of content (e.g. minify files) before they are delivered to clients.