The comments about camera angles is a very big point.
I work as a cameraman filming sports games for my local TV station, and even for a small production, there are a lot of cameras involved, and switching between them all to find the best shot is very important.
I have been thinking of some way to get better angles in TF2 to make watching streams more interesting for a while.
What's needed are several cameramen. Each team gets it's own cameraman. Each cameraman has a view of all 6 players (in first person mode) on his assigned team. He can then pick which player is doing something interesting at the time and send it up to the main cameraman. He then takes whatever camera angle is the most interesting (whether it's a first person angle of someone on either teams, or a top down overview of the map, or a "cinematic" angle from where the action is. He can then push that to the stream and the viewers and announcers can see it.
This would take a lot of work, and isn't technically possible at the moment, but it would make watching a lot more interesting.
I also believe that first person camera angles should be used less, but are still very important in order to see just how intense matches can be, or how much skill is involved in making certain shots.