I wonder what the field of study is called that prepares people for this kind of traffic management/design job and...
Civil engineering, and traffic engineering specifically.
whether is includes average driver/distracted driver/lowest common denominator design considerations.
Sort of, but not really. I'm sure there are some traffic engineers somewhere that do research on distracted driving, and their findings get turned into recommendations about signage placement and such. But I think most engineers actually doing the road design 'assume' drivers are mostly rational actors and are not overtly defensive in their design. Instead, they wait until crash data collected after the fact forces the issue.