It's just a poorly designed dragster, if it is that. For one, where would be the breaking system for it? Doesn't look to have one, unless they use the gas as a breaking system i.e. fill the tank up so it has just enough to go through the lines, then it'll loose energy once it's through or whatever.
I think the artists was just poor at understanding vehicle mechanics.
You are correct that a bike would handle the terrain better but there are also armor and trunk space to consider, which the car offers. And the fact that they are all over the place makes it much easier to find the much needed spare parts.
You have to take into consideration, the years between FO2 and FO4, and how that would effect the cars and motorcycles. Having a vehicle, doesn't mean you'd need to use it as a place of storage, what if it got blown up? All that stuff would be lost, and I doubt many people would be using their car to stash stuff, if it had the likelihood of catching fire and turning into a mini-mushroom cloud. And again, just because there's a lot of them out there (which there shouldn't be, that was Beth's doing), doesn't mean you're going to be able to find cars with serviceable parts to take off, and put them all together for one workable car. Years and elements would play a big part.
A motorcycle would be more simpler to have, because it would realistically (and in the game world), be easier to take care of and work on, than a fission powered car. You have access to the engine right there, and if you're set on having some sort of storage space, you could just have it so everything sits on the back.
http://www.onewheeldrive.net/wp-content/uploads/2009/07/P1060093.JPG