Cars didn't replace walking, they replaced horses.
I think you are begging the question - are cars more dangerous than horses? Just from reading random history, it seems like a lot of famous people were killed by riding accidents. And even today when the vast majority of people don't ride horses, I bet you can name a famous person who had a terrible accident.
Horse riding was much less popular than you think. What was much more popular was horse-powered carriages, which are much more convenient than riding, and also less dangerous. Horse riding was pretty much a hobby, a hobby of the rich at that. Try reading some books from the era. For example, in Steinbeck’s “East of Eden” there is a quite funny moment when Hamilton sons were going for dances, when two older brothers already took family buggies, the younger didn’t choose to ride on a horse, but did something quite different, which made his mother very unhappy.
Do you have any specific reason for believing the transition from horses to internal combustion engines increased casualties in the long run? Or is it just a gut feeling?
I think you are begging the question - are cars more dangerous than horses? Just from reading random history, it seems like a lot of famous people were killed by riding accidents. And even today when the vast majority of people don't ride horses, I bet you can name a famous person who had a terrible accident.