App-based folder organisation in iCloud
You aren't forced to use app-specific folders, it's just the initial setup. Why not just store things outside the app folders by dragging your existing file structure into the drive folder itself?

On OS X - iCloud drive works just the same as Dropbox. You get a folder and it syncs. Apple makes special folders for some apps and categories, but you don't have to use them. 

On iOS - in the settings app under iCloud - enable the toggle that says "Show on Home Screen" for iCloud Drive and you can browse away just like Dropbox (and other file sync apps allow).

Also - finder tags are now portable across devices, so you could use tags as well to help categorize client files no matter where they are stored on the filesystem.