The moderators do have a user account that they can use to hand out moderation more anonymously, however it is an absolute pain to use as you have to log out of the forum, and back in as the moderation team, then remember to come out again and log in as yourself. for a quick moderator response this slows things down, and we seem to be spending enough time on here as it is, especially when we have contentious threads running that we need to keep an eye on.
As far as objectivity, we are to the best of our ability neutral when it comes to moderation - each case is weighed on its own, but of course if the posters ensured that their posts were not contentious, then the moderators job would be easier, and we would not need to be objective (though we would still be objective anyway).