Exactly. If the entire game is competitive people then it'll be dead. There will be no way for it to be profitable and thus the bonus hunters wouldn't play.
Let's stop right there! If bonus hunters don't play, then is it not profitable again? 
This may be akin to stating, "it's a terrible move to bluff on the river: you shouldn't shove with nothing," yet if we keep that ideology, then it suddenly becomes a +ev move. If it's always terrible to bluff on the river and nobody does it, then would it not be profitable to do so? Your opponents would never think that you were bluffing!
But in correspondence with bustabit, this will simply result in a sort of oscillation in the number of players.
No, in keeping with the poker analogy, the bonus game would be filled with people playing GTO. You need a significant edge from the bonus to counteract the house edge on every game. If the game is only running with people who are playing "correctly", you won't be able to get that edge enough to outrun the house edge.