An obvious solution would be to allow third-party storage services where you can dump your device data pre-encrypted and restore from those services. Only you would have the key. It isn't hard to implement.

The hard part would be getting the US security apparatus to allow it. ALL major storage providers DON'T support end-to-end encryption for this reason. Not Google. Not Microsoft. Not Apple. Not Dropbox. Isn't this interesting?

Furthermore, talk of supporting end-to-end encryption is basically NOT in the Overton window in these companies as far as I know. Discussion of it is met by silence from management. It is weird when you begin to see the spider webs of power in society.

All those people positing that it this is an effort by Apple to push for end-to-end encryption are either disingenuous or wrong headed. If Apple even thought about end-to-end encryption, the whole US government would come down on Apple like a ton of bricks.

Apple has shown no recent indication of even leaning in this direction. Not only does Apple not directly support end-to-end encrypted backup on iOS devices to third parties, it precludes it from happening. You are stuck backing up to your Mac or jailbreaking.

EDIT: There seem to be a few small movements in this area. Dropbox has their Vault with pin based protection. Seems incredibly and intentionally weak.