I think the best way to explain the lack of vehicles is some lore and infrastructure. Throw in a fair number of broken down, smashed, and exploded cars and it will stop being something that's questioned.
Let's say that the government started focusing heavily on reducing emissions at some point, and to assist with that began constructing a huge rail network for public transportation. This would go beyond the simple subway system we have now, as it would be above ground. Also, buses and trolleys would be more common for local transportation needs. Bicycles may also be a fair addition, but we've discussed those before.
After the infrastructure was in place, taxes on gasoline and high emission vehicles eventually got so high that only the well-off could own cars without going broke. Tax breaks were given for carpooling (Along with an entire government site dedicated to organizing carpools), however, so it wasn't the sole property of People who wanted to avoid the taxes could also turn in their cars for cards that gave them so many credits for public transportation, which could last for months or even years, depending on the car and how much you travel. The government typically recycled these cars or gave them to different agencies as a form of funding.
It's a bit of a stretch, but it makes sense without adding metal eating monsters to the game.
Or, as an alternative idea, infected people(s) who die in vehicles eventually evolve into a creature that fills the car and is capable of operating it. Hear a loud VROOM? Better take some cover, the demon car is coming!
The best part is, the AI for these things doesn't have to be good, since they're essentially giant blobs mindlessly driving cars around and trying to hit you. These would make dangerous, entertaining, and rewarding enemies.