How is that not like Fallout at all? Explain.
What you're describing sounds very much like an elaborate survival game. Fallout isn't that. It may thematically be linked to survival, but that's a very small bit of what it is.
It is a post-apocalyptic turn-based RPG which focuses on themes of civilization reemergence, survival and life after nuclear war. A
Take away settlements, you eliminate the factor of civilization reemergence and anything pertaining to it, as well as a huge gameplay element. The original game was basically going from settlement to settlement, doing quests, while searching for clues to the main quest. Survival was an important thing - surviving radiation etc. - but it was more of a thematic element. Survival of humanity, survival of settlements, survival of your Vault - but when it comes to direct survival of your character, it was fairly limited to RPG standards refurbished - healing potions became stimpaks etc. It's just a gameplay convenience. Focusing on medicines and their scarcity was never a thing in Fallout (just to remind you, in FO2 you could make Stimpak from roots and flowers).
Also, food was never a factor. Sure, you had food, but it was fluff.
And as far as gameplay goes, Fallout can be a brutal game if you want it, or a fairly easy one. But it's not limited to either of those. Making it hard for the sake of being hard doesn't really fit it.
Don't get me wrong, I don't dislike your idea in general. A game such as you describe is a game I'd play. But the game you describe isn't really Fallout.
(Again, if you haven't, look up Neo Scavenger. In some ways it is a game you're looking for.)