This was implemented on GvG merely for the sake of turning the event easier to manage for the Gm in charge.
At the same time, it took out an important tactic many players/guilds used; spying. On GvG, a dead member of a guild could previously, tell his/her guildies of possible threaths or runaways for them to avoid/chaze, should these pass on their screens.
On the PvP room there's no need for it since its always open. And taking out the possibility of a normal player for spying on the arena will only encourage cheating.
Furthermore, a dead character inside the PvP arena will not disturb the people in there in any way. I don't see a single plus on the suggestion.