Does any file system implement Copy on Write mechanism for CP?

We have seen OS doing Copy on Write optimisation when forking a process. Reason being that most of the time fork is preceded by exec, so we don't want to incur the cost of page allocations and copying the data from the caller address space unnecessarily. So does this also happen when doing CP on a linux with ext4 or xfs (journaling) file systems? If it does not happen, then why not?