The idea of making a game focusing on a solo character which is set before, during and after a cataclysmic event such as nuclear war has never been explored before, I believe, at least not in a way of following one household, family or something similar. It definitely sounds interesting, and alluring to play, but I'm not sure how it would exactly look like, and if it is doable, at all.
Making it a shooter would probably mean making it very similar to many zombie-apocalypse games. Or more akin do Dead Space. There's that post-apocalyptic game, Afterfall: Insanity. I could see it being something like that, maybe, but from what I hear, that game didn't do very well...
Doing it as an RPG...I'm not sure. I'm not sure it's even possible, unless you're planning on making it an aRPG. I don't really see NPCs, communities, quest-givers and all that in the world struck with apocalypse basically days ago. Not to mention you probably wouldn't have a story of any sort, except maybe, "Go to the bunker on the other side of the country, it's safe there". Generally, I doubt anyone would do something like that. It's not a very attractive game for game masses, don't you think? Sure, crowd-funding is a hit these days, but I still don't see it happening.
Survival simulation? Now that's a bit different. I would personally love to play a game where the only goal is to survive in a freshly-destroyed world. Searching and purifying water, finding food and hunting, searching for tools, weapons and making such, looking for shelter from fallout, and ultimately, looking for other survivals and a place where you could continue your life safely sounds attractive to me. But that's just me. Not many people would be interesting in something like that, as it would hardly have any value except for folks who love experimental stuff like that, or are in hardcore survivalist/post-apocalyptic things. But such folks are rare. Post-apocalyptic may be in mainstream nowadays, but those are generally "mild" stuff, including Fallout. Nothing really hardcore or realistic.
I mean, a game like that would basically be empty. And grim. No NPCs, not really anything you can fight against, nothing. On the other hand, should it stay realistic, it would have to include a range of stuff which would hypothetically occur if there would be an all-out nuclear war, and that's not really practical, or achievable. In general, I don't see many folks having fun with a game like that.
Such game would truly be something experimental, an art game, aiming for niche.
And I don't see that happening...
That all being said, even though I'd personally like to see such never-will-happen game, I wouldn't want it to be set in the Fallout world. No, definitely not.
A game set in pre-War/War times would definitely kill the franchise, especially a game like this.
However, for the end, it is worth mentioning that project JE Sawyer was having on his mind several years ago, about a Fallout game set during Resource Wars, in Canada, Alaska and such...
What would you make of that?
