I can't really think of anything to let people do when they die other than spectate. Maybe they could all vote on random events to happen to the tributes, and whatever gets the most votes happens.
Rounds aren't too long. On the last map they lasted 15-25 minutes. If they go past 35+ the Gamemakers will order everyone back to the Cornucopia to fight, and if they don't head back, kill them.
And by kill them, we mean: fly after them in a massive ship shooting rockets at them until they die. It's a lot of fun for both parties and more immersive than just exploding.