Yeah, putting elimination directly in-game would be a bit over the top, but how about this?

New architecture item: Latrine (or outhouse).

Gives a comfort bonus to all players in the tribe.

Gives a comfort penalty (that is even greater than the bonus) if you're too close, however.

So you do want a latrine in your village, just not right next to your cabin. Adds a little bit of the NIMBY element to the game.