I think there is merit to having the same organizational unit badges have in the group context (eg each group can optionally belong to a group category). In fact I would expect larger numbers of groups to exist than badges.
As to when we can slot this, up to @codinghorror. The idea definitely has merit. The big open question is if we would use a “tag” like concept so groups can belong to multiple “grouping” or category like concept where groups only belong to one thing