Most of shops i visit , other family members, my job , parks etc are all within about 5km of me.
The longest drive i do to visit a family member is 90km, every few months.
Anytime i've visited the US even going to the nearest shop seemed like a very long drive.
So if all other things are equal, theres just more opportunity for accidents.
For example, the risk of a car crash should be near zero if the distance driven is also zero. But even in the safest of vehicles, driving 100KM, 1,000KM, or 10,000KM+ each are going to have higher rates of accidents assuming real-life road conditions.
In the US, on average, people need to travel further to get to their destinations, and so on average I'd expect car accident and death statistics to likewise be higher.
I'm very in favor of reducing urban sprawl, utilizing public transit, etc., but in present state the US has vast quantities of existing road networks which can't be consolidated or mitigated overnight, so the next best way to improve those statistics would be improving traffic controls, vehicles, safety features, etc.
But state and federal governments should absolute zero-in on reducing sprawl and travel distances and those actions should've started yesterday and they should stay laser focussed on reducing driving distances (especially for non-leisure reasons)
Many of the most effective and efficient measures to reduce traffic fatalities work by reducing traffic. For example, promoting public transit. However, if you measure fatalities per kilometer these highly effective mechanisms have no effect on the metric.
If I drive the approx 200 miles to central London I am at a far greater risk of having an accident in the crowded traffic of the last few miles than I am on the motorway on the way there.
One big difference between the US most of Europe is that people tend to commute by car a lot less.
In the USA, I have a friend who will do a tour visiting family every few months that takes him 1400 km outbound.