Yes, because that's how people work. Nobody was driving unsafely before, because they were afraid of their cars rolling over.
No, that's not how they work. They just died at higher rates.
Would you look at that!
https://en.wikipedia.org/wiki/Motor_vehicle_fatality_rate_in...
Turns out unsafe cars killed more people and when we started making them really safe, they stopped killing as many people, despite people driving more: https://en.wikipedia.org/wiki/Motor_vehicle_fatality_rate_in...