So, I've been kind of thinking about it, looking back to Fallout 3 and New Vegas and the travel times between places and how the overworld is set up...
I wouldn't mind a motorcycle or a mount or something, really.
You say "vehicles" and what springs to my mind is a car that can go super fast (relatively-speaking) and tear across the Wasteland. If my primary mode of transportation is a car that can go 80mph, you kind of need these big open stretches of land - just to be able to open up and drive around. I think there's absolutely potential for a Fallout set in an area that would make sense for that sort of gameplay. A region that takes place in a very open space and where it's inhabitants make use of vehicles. You could tie a lot of gameplay to keeping your vehicle running and scavenging for upgrades and even just fuel to keep going.
(There was a really great Ken Burns documentary some years ago about the very first cross-country road trip in 1903 ("Horatio's Drive," if anyone wants to check it out - it's pretty good.) It was just Horatio Nelson Jackson and his mechanic (with Horatio's dog along for the ride.) That car pretty much constantly broke down, and they were always getting mired in mud and poor roads and using whatever they had at hand to keep the car limping around. It made me think that could possibly make a great post-apocalyptic game in it's own right. A road trip would tie in wonderfully with Fallout's sense of Americana, and the scavenging and maintenance angle would be a great fit for a post-apocalyptic game.)
So yeah, a game that would make a car useful would be too big and open to be something very optional - like walking around in GTA, it would by it's own virtues be a game that required use of a car.
But then I started thinking, that most of the time when I'm exploring the Wasteland I'm running, or I'll hit caps lock and auto-run. The average travel time when I'm out in the Wasteland sort of encourages me to run instead of walk, and if I'm running then having a mode of transportation that would allow me to move at about that speed or slightly faster could make perfect sense to me. Like a run-down motorcycle that kind of chugs at maybe 25mph or so I don't think would require greatly re-arranging a game like New Vegas. An ATV of some sort would be notably suited for getting across the uneven terrain. Or a bicycle or even some sort of post-apocalyptic mount of some kind.
I could see all of those things working... pretty well, actually, for a game of the scope and size of something like New Vegas or Fallout 3. Something that didn't move so terribly fast that you'd need to scale up the size and density of the world; and if you drove to the DC ruins and then parked your motorcycle outside because it was better suited for walking around in that area, I think that would be perfectly fine, too.
Probably need some mechanics associated with it - you'd need fuel to keep it going, obviously. And a map marker so that you didn't lose it. And probably a side car so that your companion could ride along with you. I'd probably also want maybe an option so that your companion could run and fetch your bike for you - most games with mounts let you "call" your horse to wherever you are, or just have tons of vehicles for you to hijack. Since a motorcycle wouldn't be able to drive itself to you whenever you called it, it might be nice if your companions could fetch it for you.
So yeah, maybe a car would be unwieldly in a game like this (and I'm trying specifically to base this on past Bethesda Fallout games - we just don't know how big or dense Fallout 4's world map is going to be, or what it's level design looks like - how much urban vs rural area there is, etc.) But something like a motorcycle or another vehicle that moved just a bit higher than running speed - I think that would be fine, off-hand. Something that was relatively small and maneuverable and didn't take a lot of time to park and get in and out of, and didn't require so much attention just to drive and get around with that you'd be missing landmarks or other neat things, or undermine the random encounters.