Well, in modern culture most people *are* attached to their cars, and almost everybody has one unless they're in a large city like New York or Chicago.
If you're looking at assembling this as a kind of module or rule set, you're going to need a list of suggestions and scenarios designed to part PC's from their usual gear. For example, what if the zombie attack hits Cabo San Lucas or Jamaica while you are on holiday? You might own a car, but chances are you don't have it with you. A confined area like an island would give the PC's an objective - get off the island alive.
I suppose getting out of populated areas crawling with infected is an objective. Much like Twilight 2000 though, you're going to need to explain to the PC's what they have to shoot for, otherwise they're just playing for time until they run out of tinned food, shotgun shells, or gasoline. Playing for time is all well and good, for a few sessions, but if you wanted to run the 'grand campaign' taking your heroes from stage 1 through stage 3, surviving isn't enough. Like Mad Max, eventually they'll either be killed or become very successful and accustomed to surviving in their world. Humans adapt.
The challenge you are hitting comes from your source material. Movies, as much as we like them, are rarely epic in scope. They generally focus on a small group of characters over a relatively short period of time; more akin to a short story than a novel. Survival is fine in a short story, but if the characters *do* get out of town alive, with a 2.5 ton truck, three thousand rounds of ammunition, a still for fuel, and food for three months ... what do they do now?
- "Don't assume you are safe because there is a rational explanation for all of this."