Lack of fossil fuels isn't as big a problem as it would seem to be be. Anything with a carbeurator can be tuned to run adequately on pretty much anything that will burn, so pure grain alcohol would work, and gods knows how many stills there were in Fallout/2, producing more than enough alcohol to allow several "unseen" vehicles to do useful work around the various communities. Fuel injected vehicles could in theory be adjusted and modified, if they weren't suitable already (since the 1980s many "flex-fuel" vehicles were available that can burn a variety of fuels, and millitary "multi-fuel" "Deuce-and-a-half" 6x6 cargo trucks will run on litterally anything that burns, no modification, just pour it in, even mix it; though they are optomized for diesel, alcohol, gas, kerosene, home heating oil, or anything else will work). This assumes that in the Fallout timeline liquid-fuel burning vehicles were at all common by the time the war started (even if atomic vehicles had reached very high penetration levels (which the game text suggests, especially the description of the fuel cell extender from the wrecked Highwayman in Klamath Falls, there would still probably be old or even classic fuel-burning cars around.)
Precious few vehicles would be useful to the player, however. First off, anything that works on combustible fuels probably cannot hold enough fuel to travel in the wasteland, espcially if it is running on something like alcohol which doesn't have the same energy storage potential as gasoline or diesel. You'd have to carry a LOT of fuel and procure it regularly, and it would be heavy. An entire game mechanic would have to be devoted to purchase, procurement, and application of the fuel, as it would be impossible for the player to carry around in significant quantity.
Thus the player would only want to have an atomic car -hence the Highwayman is the only useful vehicle in Fallout 2. And while something might be a good vehicle, able to be used, doesn't mean the player wants it. I'm sure a farming community would go nuts over a tractor or a bulldozer, even if it ran half-assed on alcohol or its atomic power source was iffy. But what would the player want with a bulldozer? Not much, when you consider how slowly it would move, how much fuel (of whatever sort) it would use, and how frequently it would need repairs. No big deal if the bulldozer breaks down for the 4th time this week in town, just have Sparky get his tools and come out to the job site to look at it, ho hum, the workers get some time off and Sparky gets paid again. But if the player's vehicle breaks down 50 miles from nowhere squared, what's he going to do?
So the only car in Fallout 2 was a large, atomic-powered sedan, capable of carrying a lot of stuff and people (think, it's a six-place car and the max number of NPCs is 5 in normal gameplay, although I'd hate to be in the back between Marcus and Goris...) -pretty much the only vehicle useful to the player. There was no reason to show the player the working vehicles because there would be no reason for him to interact with them, but if he couldn't he'd feel cheated.