s/many more/infinitesimally less/
The number of crashes that happen with both parties following the law is practically none. Pretty much every crash is due to multiple factors, but a healthy majority of fatal crashes are caused by the big three: speeding, failing to yield and running red lights. The rest are caused by a variety of causes. Starting with what you might suspect, cell phone usage and drunk driving, and ending with random low probability stuff like heart attacks and vehicle defects.
If we just tamed the big three the US would save 15,000+ lives each year and prevent another 1,000,000 casualties.