Thank you for the suggestion! I like this idea a lot.
There would need to be changes in a few areas to make this work:
UI needs ways to mark spectator players when starting the match, plus a on/off toggle for whether additional spectators should be allowed to join once it starts
Server needs to track spectators in addition to regular players, and needs to only transmit publicly-available information to spectators
Are there any notes on expected behavior you'd like to add?
It'd be nice to display everything to all players on a tv.