Wouldn't it require constantly pushing/fetching? Or would it effectively be like a hosted thing with a service layer on top of git showing a live view of the repo's tickets? Like github but for tickets... oh wait...
Now what you are talking about seems to be about the lifecycle of a bug. With this model you can replicate the same behavior as on major bugtrackers, or also track some metadata (fix in commit xxx) and compute where the bug is "deployed". But that's a UX/social problem, not a technical one imho.