I think Fallout 3 is actually the worst example (along with New Vegas) you could bring here. In these games you knew exactly what to do, you didn't only have a main objective, you also knew where to find the breadcrumbs. That you didn't need to follow this objective is without value.
I was talking about a game that starts out without any main objective. A game that fully embraces and not only demands, but also creates the uncertainty you feel - through it's narrative and it's gameplay, as you are without any thread you could follow. The main quest would begin without you realizing it and by finding it yourself (which would be fairly easy in a game that is primarily about WAR, as Fallout 4 should be - which results in you effectively being thrown into the main quest by exploring and experiencing the world that is about this main quest).
I have a different opinion about the meaning of the title 'Fallout'. Yes, the literal fallout started right after the bombs fell.
First, the literal fallout is still around in the world even 200 years after the Day.
Secondly, the Great War is another kind of war. That would go quite well with your idea actually, since the first experience would be about you "winning" the Great War - the only winners are the survivors and even these are losers.
But most importantly, 'Fallout' is meant quite figuratively imo. It's about the aftermath of the Great War, the Fallout, that affected society, humanity and that still continued in the way history would (despite all that divergence thing) - with war. What's Fallout about? Fallout is about Fallout, us and US and war.
And imo, Fallout is not about the Great War. The Great War is a vehicle to transport us into a world that allows for interesting roleplaying. The silence that followed and the years after - these are times about survival, times of the few, not the many. These are times about struggle, combat, lawless family-tribes and great chunks of nothing, not war.