I think it could be great.
The immersion would have to be complete, the soundtrack stellar, the graphics unbelievable and the story compelling.
I really don't think you need something to jump out and kill you to make a game a challenge, but it would have to have a better challenge than simply staying alive. A time limit, sanity, starvation, heat, disease.
Trapped in a city littered with dead bodies, utterly alone.
A story tied together by radio messages, written notes and visuals which do a great job of relaying the destruction and death, but still leave the imagination open.
Maybe not so much a zombie game, but rather wondering, What the hell happened, and trying to find out.
Imagine realizing that it's only the continent you are on that's been decimated, and the last group of survivors is leaving. You have a glimmer of hope, but you have to reach them in time.
The game would have to be shortish, but could still have real gameplay elements.
As you are alone for too long, sanity might start to slip, including hallucinations, such as glimpses of monsters, shades, shadows and sounds.
Potential challenges to overcome, dealing with hordes of rats, drawn by the decaying bodies. Getting bitten by a snake, having to survive while feverish and poisoned. Finding clean water, transportation, making your way across a ravaged state.
Finally reaching the rendezvous point, only to find all the survivors dead, or long gone.
I'd play that... or rather, it might make a better book.