Survive together but only one can win
It's a design choice. It's the same reason people make games linear versus open-world. Even in level design, you might put alternate paths in the mix, but you can design the game to feel more open and still guide the player to the "right" or "intended path."
Otherwise, the game becomes more random, and thus more complex.
I really like your concept, but I feel you should also consider the theme of your game. "Survive together" implies that it is a cooperative game. From the win conditions that you've provided, I can see that it is, in fact, reasonably possible for at least half of your players to win. So is it necessary to include the element of subliminal competition?
In my opinion, you should allow your players to decide whether or not they want to work together instead of including it in the package. If some want to compete, they will compete. If some don't, they won't. If you are making a survival game, the objective should be to get as many players as possible to the end of the game. The gameplay would still be interesting, because the players have conflicting goals and the freedom to choose their allies based on that.
Someone mentioned game theory, and that brings up thoughts of the Prisoner's Dilemma. I would look into that.
Again, that is only my opinion. If you release this game, I would be interested in playing it. Best wishes!