Yuki does pull her weight, though. Just in a very different kind of way.
Without her, most likely the other two would have gone crazy.
She is just as important as Kurumi's shovel or Yuri's management/motherly skills.

As far as they know, they're the last living people in the city/country. Yuki helps them find something to live for when there's nothing left in the world. It is the reason they can decide to just live at the school instead of trying to leave and find surviving civilization, if there is any.