Spectator Mode / Team Deathmatch
Thinking further, the most obvious state to be in after dying would be a kind of spectator mode. Even if there is no team deathmatch, I realized, a spectator mode would be a useful thing to have. It beats sitting around giving out free flags in nexus, and would be helpful for recording important events. There are two kinds of spectator mode I can think of, one where you are free to scroll around like you were a ship, but invisible and intangible. Perhaps you would be limited by barriers, but maybe not as it is important you could not interact with the game. If not, however, it would probably be important to limit how far away from the game you could wander. The other kind of spectator mode, which would be the most sensible for after death in team deathmatches, would be to view the screen of a teammate. This might be easier to implement, because you wouldn't have to worry about barriers, but maybe not.
In any case, these things would be nice but I'm not sure they are necessary. Spectator mode seems more useful. What do you think?