The usability implications of not being able to access information if you lose track of the link will be enough to ensure this never takes off, let alone the vast security holes.
You can do this with an app like VeraCrypt https://veracrypt.codeplex.com for DropBox or SyncDocs https://syncdocs.com for Google Drive.
Relying on cloud providers to protect your data is not a great idea - just ask Hillary Clinton about Podesta. Adding a separate layer of security and another means of authentication is more secure.