The only game I know where you have to consider parking is “Workers & Resources: Soviet Republic”. I haven’t provided any private cars to the people from my Republic yet. But from what I have seen, you need to provide parking lots close to their home and their destinations.
I think it simulates each person going to their (a?) car and driving this car to another parking lot with free spots. So they do really fill up. However, I do not have first hand experience. In our glorious republic walking an public transport is all we need. So not even the most loyal party members get cars.