We would love to add the Mac App Store as a distribution channel for CCC, but there are certain classes of applications that do not meet the policy requirements imposed by Apple. Unless Apple changes these policies, you will never see a utility that can make a bootable backup of macOS on the Mac App Store. You can send Apple some feedback about this policy, but judging from the absence of the Mac App Store from Apple's Feedback page, and Apple's pertinacious position on this matter, we don't anticipate a change in this policy.
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This documentation is for an older version of CCC.
You can find the latest version here.
Last updated on April 23, 2018