Another factor might be that red counties are more likely to be rural and further away from major medical centers with all of their specialists. When minutes can be the difference between life and death, it makes a difference whether the emergency room is ten minutes away or twenty minutes away.
And yet another factor is that rural 2-lane roads have a very high accident rate compared to urban roads.
Here in Virginia, they are hilly, windy, and almost never have any shoulders, and many of the intersections don’t provide a very good view of oncoming traffic owing to the fact that they’re in the middle of a curve or they’re not at a 90 degree angle or other piss-poor examples of highway engineering.
Not that most of these roads were actually engineered. The improvements stopped when they got paved.