While I can see where you're coming from, I don't feel it's the group so much as it is the individual group members. In my opinion, by muting the user (who is possibly the source of all your misery), you can effectively mute the group, or at the very least the low-quality posters within that group.
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Sure, but there are groups that have formed that exist only to create troll threads. Rather than going through and muting each user, I could just mute the group and be done with it. The other way it would help is content filtering. Say there's a user who posts a lot of fan fiction. Personally, I don't care for fan fiction, and so I mute users who post it. Unfortunately, that means I can no longer see any non-fan fiction threads the user posts. If there was a group for fan fiction, and users just posted their fan fiction in the group, I could mute the fan fiction without also muting all the posts from those users.