Posting bounties is not a particularly difficult, time consuming, onerous, or critical task. If it doesn't get done, then it doesn't get done, and nothing particularly bad will happen. A region lord doesn't need to be in his region to do it. He doesn't even have to be in his realm, or can even do it while traveling. (I just did it, to make sure.) If he doesn't do it, it's his own region that gets stomped.
Given all that, and the fact that bounties don't really have anything to do with justice or law, I personally don't really see anything that would justify the judge being able to do it.
