Even though the actual spectator mode matches more the "spectator stuff" I think being able to play the game as a character while other players are fighting, like in 1.09.4's spectator mode, was really cool and I think if gametypes like coop ever have an spectator mode it could be useful for some new players since they could be training some jumps and learning how to not die.
I like the idea of a spectator mode for multiplayer gametypes in general that allows the player to control a "ghost" character. While on the "Spectator" team, the player has "You are a spectator, press (insert whatever button the player has bound to spectate here) to view others players" displayed on their screen for long enough to read.
While on the spectate team, the player could have the following traits:
-Moved to spectate team when getting a game over.
-Appears transparent to themselves, indicating they are a ghost.
-Cannot be seen by other players except others in the spectate team, who see them as transparent.
-Can bounce off enemies/monitors, but cannot deal damage to/break them.
-Cannot pick up rings and other collectibles (Emerald Tokens, CTF flags, etc).
-Cannot interact with other players.
-Cannot trigger the end of level flag (End signs, etc).
-Is immune to all forms of damage except crushing and bottomless pits.
-Can breath underwater and in a vacuum.
-Has infinite lives.
-Dying does not impact score in any gametype.
-While spectating a "living" player, you can only see what they can see (Cannot see spectate team players).
-Can only text chat with other spectate team players.