Make a certain amount and variety of monsters appear at the beginning of the match, no respawning. They're meant to be hazards and will not drop loot or XP. However it will allow skills and traits that take effect when killing something to be more useful. And watching out for the enemy player who isn't too far away is part of the game.
Players controlling monsters: Absolutely not. Monsters are NPCs only. Plus blizzard would have to balance monsters even moreso and make a new UI for any creature a player would control.
Q u o t e: Friend: Trolling the forums?
Me: No, Controlling the forums.