iirc, you could salvage a car in FO2. doing so increased your fast travel time.
something similiar could be done for fo4. dont let us actually drive the car in realtime, but make it clickable to quicktravel. make the trunk interactable so we can store supplies or loot. followers could also always be passengers in the car, making it easy to switch to a given follower depending on the location.
maybe require some kind of resource to use it (i think the fo2 car required energy cells). could be tied in with settlements, i.e. settlements provide fuel resources and/or increase the radius in which you can use the car to fast-travel, and as you upgrade / create new settlements, the radius becomes larger.
the ability to "call in" the car to a given location could also be added. lorewise you could explain it by calling one of your followers to come pick you up or something. that'd solve the issue of having your car available even if you didnt use quicktravel to reach a certain location. i really dont like using quicktravel, especially in the beginning. it makes the world seem small and instanced.
if they really wanted to make it immersive, the car could be driven by an npc on fixed routes. kinda like taxi points in world of warcraft, no need for collision detection or the likes. this would also be a very cool DLC feature.