Cars in rural settings are generally faster and more indispensable for their owners. It is much easier to enact policy that reduces car traffic in cities than in villages.
It makes a pretty big difference. Yes, the opportunities in the city are bigger for everything, but so are the dangers. The amount of crazy people. The effort involved in getting to a nice and safe place where the kids can just run around without you having to watch them every second. Those places also exist in some cities, but way too few. So great that you don't have a car, (I mean it) car free places in cities I do enjoy, there are just not many of them.
I have two three year olds. Parks where they can run around with relaxed supervision are not far. A big park is close enough that they can walk the distance and in less than half an hour by bike we can reach a forest and four or five other parks.
Then your reply "Most of those opportunities involve getting hit by a car." is somewhat weird. This wasn't the case even in my own backwards country of Moldova in the 90s, after the fall of Soviet Union, much less today, when people are noticeably more civilized.
1. The people actually obey rules (e.g. they actually let people pass at pedestrian crossings, something unheard of all the way into the 2000s). In general road accidents are decreasing.
2. Still doesn't support your "Most of those opportunities involve getting hit by a car."
Most of those opportunities involve getting hit by a car.