Move Git VCS Label

TeamCity has a VCS feature to automatically label VCS roots.  Normally, these labels contain the build number or some other uniquifier so that each build produces a new label.  However, I would like to move an existing label to track the commit pertaining to the latest passing build.  The VCS Labeling documentation has this to say, though:

"Moving" labels (a label with the same name for different builds, e.g. "SNAPSHOT") are currently supported only for CVS.

What is the reason for this limitation?  I would like to apply this concept to a Git repository.  I realize moving Git tags isn't standard practice, but it is possible.  Even better would be the option to use a branch instead of a tag and move that to the current commit on a passing build.  Would this be a feasible enhancement?