No, let's not remove that, for now.
There is a difference between badges and privileges. Badges have always existed to award and stimulate positive behavior. The badges are modeled such that users are encouraged to use specific functions of the site, to help establishing the goal of being a repository of knowledge.
It is important to show those badges and who earned them and with what, for example altruist. When other users see that they might decide to do a similar thing. They are actionable.
For privileges the story is much more difficult. Specially because getting reputation is not something you can directly influence. Reputation and the privileges that come with it only happen to you because you're trusted by your fellow users. You can't create reputation and with that privileges. You can only edit and post and then hope that others value your contribution on its merits.
It also doesn't make much sense to show which users just gained the privilege to vote down, or create a chat room. So there is no interesting follow-up that can trigger a user to do an action. Privileges are much more static and only a fact of life.
That said: I think the badges deserve their place in the menu. I'm sure privileges shouldn't be there as it will sent the wrong message (reputation is important! it is not ...). When there are new items that need a place on the tab menu, I can live with it if badges is being removed as an item, assuming it is going to be replaced with something more awesome.