As the title says, should meta.stackoverflow.com have badges?
Sure, why not? A higher reputation on this site indicates that one cares about SO and adds to the debates about how SO can be improved. Something similar can be argued w.r.t. badges.
On the other hand: most people coming here will be SO members already, so they don't need the addictive effect that badges have on new users.
In meta-discussions, reputation score, badges, upvotes and downvotes all lost their sense.
The point of badges is to encourage good behaviors, and that's just as important here on the meta site as it is on the main site.
I'd vote for a "Meta" badge that you get once you got enough "normal" badges. Maybe like 20 badges give a bronze Meta badge.