Recording the current branch on each commit?

Currently, git records a checksum, author, commit date/time, and commit 
message with every commit (as get be seen from 'git log').  I think it 
would be useful if, along with the Author and Date, git recorded the 
name of the current branch on each commit.  The branch name can provide 
useful contextual information.  For instance, let's say I'm developing a 
suite of games.  If the commit message says "Added basic options 
dialog", it might be useful to see that the branch name is 
"pacman-minigame" indicating that the commit pertains to the options 
dialog in the Pacman minigame.  Basically, I'm saying that well-named 
branches can and do carry useful contextual information that oughtn't to 
be thrown away.  Currently, when you delete that branch, you lose the 
branch name altogether.

So what do you think?  Would it be good to have a patch to add this feature?

-- 
Best regards,
Jeremy Morton (Jez)