How far do you feel this right should extend? Have you ever driven on a busy college campus before? Or in a parking lot? I don't think a cars' "right" to the road, as you put it, should over take safety.I don't think you appreciate or fully understand how much force you control behind the wheel of a car. Or the otential harm the person on foot is in trying to traverse our man made jungles of concrete and steel.
Here is my opinion on this issue outside of the silly strawman argument that pedestrians across america don't have a self preservation instinct. This country is build to accommodate cars. We tore up our cities making room for freeways, we created parking spaces out of parks and built our infrastructure catering to personal vehicles. We made it almost impossible, thanks in large part to urban sprawl, to travel for basic necessities without a car. Car culture is so deeply ingrained in American culture, they have become inseparable. In this process, drivers have become extremely entitled. When the entire system is built to accommodate their needs, it's not difficult to see how this occurred.
Car culture and the infrastructure that perpetuates it has blinded drivers to the plight of people trying to traverse an environment not built for them. The idea that it is too great of an inconvenience for the ones encased in speeding steel to slowdown or (God Forbid!) stop for completely defenseless people trying to get from one side of the road to the other is quite literally insane. The idea the greater responsibility for everyones safety shouldn't fall on the shoulders on ones with all the power, speed and momentum is systematically accepted insanity.
You're traveling in a machine which has killed more Americans than all American wars combined (3.2 million have died in car related accidents, but that statistic is from 2012). Act like it. When I'm crossing the road, I'm at the mercy of your car. Totally and completely. Respect the amount of power you wield and pay attention. The car is the deadly variable in this equation.