I often find in various software development uses of bugzilla that a bug is reported, may people find their way to the cc list, and eventually it comes to light that what people thought was one bug is actually two bugs. It may be that only down at comment #57 are we clear what's going on. One thing to do at this point is to file a new bug or clone a bug. But this has adverse side-effects in the aforementioned case such as the Reported Date being brand new, which may mask the fact that comment #2 on the bug was reported two years ago (this will skew reports, performance metrics, fix evaluation priorities, etc). Also, the history is only available by visiting another bug. cc: members may miss a mail and wind up on the wrong bug, etc. One way to improve this would be to have a feature to 'split a bug'. It would copy over everything about one bug, aside from its bug number, into a new bug, and then drop a comment on the new bug that it was split from the old one. At that point, the cc: list won't miss any action, they can unsubscribe from one of the bugs if it turns out only one was relevant to them, the owner can re-assign the split to a new owner, etc. This is similar to, but has a distinct use case from, 'clone a bug'.
Technically, I see no difference between your request and cloning a bug. Cloning a bug already does everything you are mentioning here, including copying the CC list.