There's two things I've (and others have) noticed by now. One, there hasn't been a Queen's Wrath event for a long time. And Two, Destiny doesn't seem to let friends play deathmatch against each other. (I haven't tried bringing a fireteam into free for all, so I could be wrong here.)
It seems like Bungie could kill two birds with one stone here and introduce a Queen's Arena event. A PvP event like the Iron Banner, but instead of being a team deathmatch event, it could be a free-for-all deathmatch event. Like a normal Rumble, but it could allow fireteams to join together (or not) if they want. So friends could have an official way to play against each other.
Lore-wise, the Reef is neither good nor evil. They're a gray area between dark and light. The Queen probably doesn't just see the Fallen, Hive, etc as her enemies. The Guardians, while maybe on good terms with the Reef, are still a potentially threatening faction to her.
The Queen's motive for holding this event could be to study the combat prowess of the Guardians so she knows what she's up against should the Reef ever have to go to war with the Guardians. But since she's so aloof, she doesn't feel the need to sneak around about it. She openly calls upon the Guardians to fight for her amusement and enlightenment, and offers prizes in return.
Reputation gains lore-wise could be the Guardian proving himself/herself to the Queen, and the vendor items her emissary sells are her way of providing an incentive for the Guardians to fight.
And in fitting with this new feature, some of the bounties could be specifically for playing against your friends a number of times or killing your friends a certain number of times.
In fitting with Destiny's idea of knowing where someone's been by what they're wearing: When you see someone wearing Queen's Arena gear, you know they probably had to kill their own friends and clan-mates to get it.
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No! Please, I do not want PvP for Queen's Wrath. I want it to stay (and become moreso) a PvE event.