That can be attributed to three things;
1 - Using Disk Utilities to make a Clone of the drive will not work - period
2 - Specific to Big Sur macOS 11, Monterey macOS 12, Ventura macOS 13, the Operating System resides in a Sealed and Read Only Volume that can not be opened by the User. Only Apple can do this and usually does some when there is a update or when upGrading to newer versions of macOS
3 - Even the Developer of a Clone Software called Carbon Copy Cloner as mentioned the ASR functionality is a Best Effort basis
Reference below
https://bombich.com/kb/ccc6/macos-monterey-known-issues