It is worth noting that iCloud allows encryption of your data using a passphrase (Usually the device passphrase but I believe you can set a custom one, if you prefer).
Apple's law enforcement guidelines[2] provide more detail about what Apple effectively has access to and can/will provide upon presentation of a warrant.
(As of iOS 9.3 and macOS 10.11.4, it appears that notes that you explicitly password-protect in the Notes app are also encrypted with a user-supplied key to which Apple has no access. They don't explicitly mention this functionality in [1] or [2], but they do imply that this is the case in [3].)
There have been rumblings [4] since the San Bernardino case that Apple is considering providing what you describe, so that users can provide their own encryption keys for their iCloud content and backups, such that Apple no longer has access to the plaintext. However, Apple has not implemented this functionality yet, and I haven't heard anything about it since the FBI dropped its case against Apple in this matter.
[1] http://www.apple.com/privacy/approach-to-privacy/
[2] https://www.apple.com/legal/privacy/law-enforcement-guidelin...
[3] https://support.apple.com/en-us/HT205794#forgot_password
[4] [paywall] http://www.wsj.com/articles/in-beefing-up-icloud-security-ap...
Most people use the same cloud storage on their desktop or phone anyway too.
(also sp. caveats, warrantless)
For companies, they have data loss prevention policies in work-enabled devices, constraining work data to only be possible to download to work-approved (usually from their MDM provider) applications, not possible to export and able to be remote wiped from the device by the company at any point they chose.
For government, storing classified information in the cloud is already a major violation. Even data designated as FOUO requires special considerations (Although AWS GovCloud is a good solution for serving such needs). In a sense, your "private clouds" estimate is already the path that has been taken, as there are many frameworks and requirements that have been created by gov over the past few years in terms of storing certain types of information. Trying to force all cloud providers to abide by them seems like it would be a losing battle as well, and would not be taken lightly by many.
But what I found most worrying was the lack of acknowledgement that exclusively using cloud storage has caviates associated with it. Are we really so comfortable with, unencrypted, cloud storage now that we don't even mention the potential for warrentlsss access and other abuses?