I apologize to all here, and Mr. Bombich and his associates, in particular, for over-generalizing my data-restore experience as well as their advice. I have removed most of my comments, and will attempt to restate my experience more concisely.
Earlier this month, I suddenly realized I had gone from having three complete copies of my data, all on distinct physical devices, to only a CCC disk-image on a HFS+ spinner created with a CCC “Task” configuration almost a decade old. If I had been keeping up with the real implications of SIP, Sealed System Volumes, APFS, etc., I would have known this was at best, not the most reliable configuration under recent versions of macOS, particularly for the scenario of “your entire Mac from a backup, i.e. to a clean installation of macOS.”
When I tried to use CCC to restore the disk-image, it instructed me to use Migration Assistant. I could not find the disk-image with Migration Assistant. Somehow (panic had been creeping in a paragraph ago) I got CCC to partially restore the disk-image. Most third-party apps, Keychain and Safari passwords, etc. were not restored. Fortunately, I was able to reinstall my apps from *.dmgs, etc., and piece-by-piece put it all back together. Helpfully, the disk-image would still mount in the Finder. Ultimately, I believe none of my personal data was lost.
As Mr. Bombich has pointed out, there are numerous scenarios that do not require Migration Assistant to restore a CCC archive. Rob in CCC tech-support was very responsive, and helpful, advising me how to set-up my particular backup needs so this didn’t happen again. I, unfortunately, generalized his advice to other scenarios.
In my case, I used a badly out-dated backup configuration in a likely worst-case scenario (aka. user error - panic can do that).