Why Do Birds Fly Low Over Roads

The only thing I can think of is a wind tunnel effect. The moving air around the car is MUCH quicker than the 5 - 10mph gusts in free air. So swooping under/over/near a car where the wind is moving 35mph+ (depending on the vehicle speed), may help to give them a bit more speed (like a glider.) So temporarily they can fly with a lot less drag and not have to use as much energy to fly. But as for the birds hitting the vehicle, just sounds like they weren't quick enough to go under, around, or over the vehicle.

I have asked many times why birds suddenly fly down as trying to fly under the car and often get splattered on the grill mesh. I never got a satisfactory answer. Sadly your answers also just aren't right somehow.
Why don't birds fly UPWARDS instead of flying as if to just miss the bumper? I wonder if they see the car as a huge predator, and they go low because predator seldom are accurate enough to catch something down near their feet.

It's a fascination of mine....

Another reason may be that any smaller bird crossing a road becomes more vulnerable to attack from predatory birds, the dive is a dodge across an unprotected space.

There are two reasons that they fly low over roads.
1- They approach the areas where they find easy food.
2- You are saying correctly that they also feel like playing and dogging the cars etc.