Yup, when the pre-release images of Route 4 and the Skyarrow Bridge started coming in, people started speculating that we would get to drive some cars.
Here's the thing with cars, though. The routes would have to be specifically designed to accommodate for you being in a vehicle of that size, and I think that would feel kind of weird. Paved roads and highways means little to no tall grass, after all. And there would probably be significantly less NPCs in areas where you could drive, including cities. The routes/cities would have to be designed around the car lanes, instead of just...being Pokémon routes/cities, I guess.
Now, they could do something like in X & Y where a few routes were accessible only by riding a Pokémon; so in this case, a few routes have you driving a car. But people seemed to not like those routes in X & Y, and I'd assume it's because they were very visually unappealing and just boring to navigate overall. I think something similar would come about if it was the same but in a car.
Speaking of riding your Pokémon in X & Y, I'd honestly rather they refine and polish the "mount" system of X & Y than get a car in these games.
Although, that "Pokémon Center Van" is definitely intriguing. Maybe it will appear randomly on routes to help you heal your Pokémon? I think that would be cool.