Sounds like the procedure you describe might work actually.
Unfortunately, it seems I was wrong.
I think your question is a very important one. It bothers me that I don't know to restore a recent macOS system to its working state as of a week ago (for example). So I tried my proposal (the procedure can be quit before any actual data is transferred). Note I am still running Monterey (12.7.5).
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Mounting the CCC snapshot is easy in Disk Utility -- no problem there (use View-->Show APFS Snapshots, select the desired snapshot, right-click and select Mount). The snapshot gets a volume name like "your-volname@snap-104098" and you can see it in '/Volumes'.
I started Migration Assistant. It warns that all apps will quit, asks for your (admin) password, asks "How do you want to transfer your information?", and I selected "From a Mac, TM backup, or
Startup disk."
The next screen shows appropriate disks: my CCC backup volume was there, but
the previously-mounted snapshot was not in the list. Boo. :-(
There is a clickable link, "Other Server", in which you can put a URL like 'afp://some-server', but that doesn't help any. I selected my CCC backup volume, and it dutifully sizes the Apps and user accounts that I can transfer, but of course that would restore only the
most-recent CCC backup, not an older one like we're trying to do.
I clicked the "Back" button, and was left at the login screen. From this (and the missing snapshot, and logic), I conclude that MA logged out of my account, and at that time (probably) the snapshot was ejected.
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As far as I know, using Migration Assistant with a Time Machine backup volume also does not let you pick a date/time in the past, instead it just transfers from the most-recent backup. (Someone please tell me I'm wrong?) IMHO this is a major flaw
in both TM and CCC backup schemes using MA to restore (if I'm correct). Sure, either system will allow you to restore individual files and folders from older backups, but what if you don't know what files should be restored to make your system operational like it was, for example, a week ago?
EDIT: I guess using CCC to restore (and not MA) is the answer?
So far, I have not figured out a way to use MA with a backup volume snapshot. I suspect there is some way. Maybe there is a way to revert the backup volume to match a specific snapshot (but even if there is, you'd presumably lose some snapshots). Another possibility might be to mount the snapshot on a remote Mac, share it, and access it via the "Other server" button over SMB. But that's pretty inconvenient. Or copying the entire desired snapshot to another suitable drive (ugh).