Watched deer many times wait in the bush out of sight and cross after vehicles pass. I have completely different opinion than yours when it comes to vehicle vs foot noise especially with mule deer. If you are on a steady pace walk yes the clue in because animals don't walk like that. If you are slow few steps and stop I find mule deer very forgiving and at times their curiosity will cause them to seek out what is making the foot steps
Mule deer have a natural flaw other deer species don't as well they will actually stand their ground and fight off predators at times. When it comes to man and they debate this tactic not knowing what you are they often offer a shot opportunity.
The only advantage road hunting has is the ability to cover ground. Instead of hunting a handful of deer you can drive through enough areas that can hold over 100. If you lack knowledge of an area and are not good hunting on foot road hunting may very well be the better option